{"id":35170,"date":"2023-10-22T16:59:06","date_gmt":"2023-10-22T16:59:06","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=35170"},"modified":"2025-10-31T07:47:13","modified_gmt":"2025-10-31T07:47:13","slug":"isosceles-obtuse-triangle-definition-formulas-examples-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/isosceles-obtuse-triangle","title":{"rendered":"Isosceles Obtuse Triangle \u2013 Definition, Formulas, Examples, FAQs"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-2600c8d2-daa7-4964-a9d9-08104c36f651\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/isosceles-obtuse-triangle#0-what-is-an-isosceles-obtuse-triangle-in-math>What Is an Isosceles Obtuse Triangle in Math?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/isosceles-obtuse-triangle#3-isosceles-obtuse-triangle-formulas>Isosceles Obtuse Triangle Formulas<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/isosceles-obtuse-triangle#5-how-to-construct-an-obtuse-isosceles-triangle>How to Construct an Obtuse Isosceles Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/isosceles-obtuse-triangle#8-solved-examples-on-isosceles-obtuse-triangle>Solved Examples on Isosceles Obtuse Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/isosceles-obtuse-triangle#9-practice-problems-on-isosceles-obtuse-triangle>Practice Problems on Isosceles Obtuse Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/isosceles-obtuse-triangle#10-frequently-asked-questions-about-isosceles-obtuse-triangle>Frequently Asked Questions about Isosceles Obtuse Triangle<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-an-isosceles-obtuse-triangle-in-math\">What Is an Isosceles Obtuse Triangle in Math?<\/h2>\n\n\n\n<p><strong>An isosceles obtuse triangle is a triangle in which one interior angle is an <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/obtuse-angle\"><strong>obtuse angle<\/strong><\/a><strong> and the remaining two angles are equal and <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/acute-angle#:~:text=An%20angle%20with%20a%20measurement,an%20acute%20angle%20is%20formed.\"><strong>acute<\/strong><\/a><strong>.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"307\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/isosceles-obtuse-triangle.png\" alt=\"Isosceles obtuse triangle\" class=\"wp-image-35186\" title=\"Isosceles obtuse triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/isosceles-obtuse-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/isosceles-obtuse-triangle-300x149.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>An <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/isosceles-triangle\">isosceles triangle<\/a> is a triangle which has two equal sides and the angles opposite to the equal sides are also equal. It has properties of both obtuse and isosceles triangles.<\/p>\n\n\n\n<p>The question here is \u2013 Can an isosceles triangle be obtuse? Yes! An isosceles triangle can be obtuse!<\/p>\n\n\n\n<p>If the third interior angle (non-equal angle) in an isosceles triangle is obtuse (lying between 90\u00b0 and 180\u00b0), it is called an isosceles obtuse triangle. Note that the obtuse angle is made by the two equal sides.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"346\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/an-example-of-an-isosceles-obtuse-triangle.png\" alt=\"An example of an isosceles obtuse triangle\" class=\"wp-image-35187\" title=\"An example of an isosceles obtuse triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/an-example-of-an-isosceles-obtuse-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/an-example-of-an-isosceles-obtuse-triangle-300x167.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/answer-questions-related-to-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_tri_on_side_pt.png\" alt=\"Answer Questions Related to Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Answer Questions Related to Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/classify-triangles-and-rectangles-as-closed-shape\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_triangle_rectangle_2_pt.png\" alt=\"Classify Triangles and Rectangles as Closed Shape Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Classify Triangles and Rectangles as Closed Shape Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/classify-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_triangles_pt.png\" alt=\"Classify Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Classify Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-if-the-given-angle-is-right-acute-or-obtuse\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_identify_type_of_angle_pt.png\" alt=\"Identify if the Given Angle is Right, Acute or Obtuse Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify if the Given Angle is Right, Acute or Obtuse Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-the-type-of-triangles-based-on-angles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_tri_on_angle_pt.png\" alt=\"Identify the Type of Triangles Based on Angles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify the Type of Triangles Based on Angles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-triangles-and-rectangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_amusement_park_18_20_gm.png\" alt=\"Identify Triangles and Rectangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Triangles and Rectangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-triangles-and-squares\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_triangles_squares_pt.png\" alt=\"Identify Triangles and Squares Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Triangles and Squares Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-types-of-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_types_of_triangles_pt.png\" alt=\"Identify Types of Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Types of Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/match-triangles-and-squares\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_amusement_park_4_5_gm.png\" alt=\"Match Triangles and Squares Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Match Triangles and Squares Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/triangles-and-rectangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_triangle_rectangle_1_pt.png\" alt=\"Triangles and Rectangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Triangles and Rectangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            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});\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-isosceles-obtuse-triangle-definition\">Isosceles Obtuse Triangle Definition<\/h2>\n\n\n\n<p>A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/triangle\">triangle<\/a> that has two equal sides (thus, isosceles); and one interior angle lying between 90\u00b0 and 180\u00b0 (hence, obtuse) is called an isosceles obtuse triangle.&nbsp;<\/p>\n\n\n\n<p>The obtuse angle lies opposite to the longer side, and the other two angles are acute on equal sides.&nbsp;<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/rectangles-and-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/rectangles-and-triangles.jpeg\" alt=\"Rectangles and Triangles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/separate-out-the-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/separate-out-the-triangles.jpeg\" alt=\"Separate Out the Triangles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-isosceles-obtuse-triangle-properties\">Isosceles Obtuse Triangle Properties<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>One interior angle is obtuse. Remaining two angles are acute and equal in measurement.<\/li>\n\n\n\n<li>Two <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/sides-of-equal-length\">sides are of equal length<\/a>.<\/li>\n\n\n\n<li>Angles opposite to the equal sides are equal.<\/li>\n\n\n\n<li>The obtuse angle lies opposite to the longest side.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-isosceles-obtuse-triangle-formulas\">Isosceles Obtuse Triangle Formulas<\/h2>\n\n\n\n<p>There are several formulas of an isosceles obtuse triangle, such as, area, perimeter, semi-perimeter, height, etc. Let\u2019s discuss different formulas associated with the isosceles obtuse triangle.<\/p>\n\n\n\n<p><strong>Height of an Obtuse Isosceles Triangle<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"330\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/height-of-an-isosceles-obtuse-triangle.png\" alt=\"Height of an isosceles obtuse triangle\" class=\"wp-image-35188\" title=\"Height of an isosceles obtuse triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/height-of-an-isosceles-obtuse-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/height-of-an-isosceles-obtuse-triangle-300x160.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Consider the isosceles obtuse triangle \u25b3ABC.&nbsp;<\/p>\n\n\n\n<p>To calculate the height of the triangle, we use the following formula:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><tbody><tr><td>Height of isosceles obtuse triangle $= \\frac{1}{2} \\sqrt{4a^{2}\\;-\\;b^{2}}$<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Here,&nbsp;<\/p>\n\n\n\n<p>h is the height of the triangle<\/p>\n\n\n\n<p>a is the length of two equal sides&nbsp;<\/p>\n\n\n\n<p>b is the base of the triangle (the length of the unequal side)<\/p>\n\n\n\n<p><strong>Perimeter of Obtuse Isosceles Triangle<\/strong><\/p>\n\n\n\n<p>The <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/perimeter\">perimeter<\/a> of a triangle is the sum of the measure of all three sides of the triangle. The formula for perimeter of the isosceles obtuse triangle is as follows:<\/p>\n\n\n\n<p>P = a + a + b&nbsp;<\/p>\n\n\n\n<p>P = 2a + b<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><tbody><tr><td>Perimeter of isosceles obtuse triangle =&nbsp; 2a + b<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Semiperimeter of Isosceles Obtuse Triangle<\/strong><\/p>\n\n\n\n<p>The semiperimeter refers to half of the perimeter. The semiperimeter of an obtuse isosceles triangle is given by the following formula:<\/p>\n\n\n\n<p>S $= \\frac{2a + b}{2}$<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><tbody><tr><td>Semiperimeter of isosceles obtuse triangle $= \\frac{2a + b}{2}$<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Area of Isosceles Obtuse Triangle<\/strong><\/p>\n\n\n\n<p>There are three methods to find the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/area\">area<\/a> of an obtuse isosceles triangle:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Area of Isosceles Obtuse Triangle Using Base and Height<\/strong><\/li>\n<\/ol>\n\n\n\n<p>We can calculate the area of an obtuse isosceles triangle with base b and height h as<\/p>\n\n\n\n<p>Area $= \\frac{1}{2} \\times b \\times h$&nbsp;<\/p>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li><strong>Area of Isosceles Obtuse Triangle Using Heron\u2019s Formula<\/strong><\/li>\n<\/ol>\n\n\n\n<p>Heron\u2019s formula is used to calculate the area when we only know the lengths of the three sides of a triangle.<\/p>\n\n\n\n<p>A $= \\sqrt{s(s \u2212 a)(s \u2212 b)(s \u2212 c)}$<\/p>\n\n\n\n<p>Here,<\/p>\n\n\n\n<p>s is the semiperimeter.<\/p>\n\n\n\n<p>a, b, and c are triangle sides.<\/p>\n\n\n\n<p>In the case of an isosceles obtuse triangle, two of the sides are equal (a = b). So, we write&nbsp;<\/p>\n\n\n\n<p>A $= \\sqrt{s(s \u2212 a)^{2}(s \u2212 c)}$<\/p>\n\n\n\n<p>A $= (s \u2212 a) \\sqrt{s(s \u2212 c)}$<\/p>\n\n\n\n<ol start=\"3\" class=\"wp-block-list\">\n<li><strong>Area of Isosceles Obtuse Triangle Using Apex Angle<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"369\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/obtuse-isosceles-triangle-showing-the-apex-angle.png\" alt=\"Obtuse isosceles triangle showing the apex angle\" class=\"wp-image-35189\" title=\"Obtuse isosceles triangle showing the apex angle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/obtuse-isosceles-triangle-showing-the-apex-angle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/obtuse-isosceles-triangle-showing-the-apex-angle-300x179.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>The apex angle (obtuse angle) is present between two equal sides of the obtuse isosceles triangle. The formula of the area using the apex angle is as follows:<\/p>\n\n\n\n<p>A $= \\frac{1}{2} a^{2} sin\\theta$<\/p>\n\n\n\n<p>Here,<\/p>\n\n\n\n<p>is for the apex angle.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-isosceles-obtuse-triangle-lines-of-symmetry\">Isosceles Obtuse Triangle Lines of Symmetry<\/h2>\n\n\n\n<p>An isosceles obtuse triangle has only one line of symmetry. It coincides with the bisector of the apex angle (obtuse angle) formed between the two equal sides. It divides the triangle into two identical halves that are mirror images of each other. If you fold an obtuse isosceles triangle along the line of symmetry, two parts will superimpose on each other.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"349\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/line-of-symmetry-in-an-Isosceles-obtuse-triangle.png\" alt=\"Line of Symmetry in an Isosceles Obtuse Triangle\" class=\"wp-image-35190\" title=\"Line of Symmetry in an Isosceles Obtuse Triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/line-of-symmetry-in-an-Isosceles-obtuse-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/line-of-symmetry-in-an-Isosceles-obtuse-triangle-300x169.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-how-to-construct-an-obtuse-isosceles-triangle\">How to Construct an Obtuse Isosceles Triangle<\/h2>\n\n\n\n<p>Let us consider constructing an isosceles obtuse triangle with two 30 degree angles and a 120 degree angle. Follow the steps given below to construct an obtuse isosceles triangle:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Draw a baseline segment AB.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"370\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/line-segment-ab.png\" alt=\"Line segment AB\" class=\"wp-image-35191\" title=\"Line segment AB\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/line-segment-ab.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/line-segment-ab-300x179.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Draw an arc by placing the compass at A keeping a suitable radius.&nbsp;<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"370\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/constructing-an-arc-on-a-line-segment-ab.png\" alt=\"Constructing an arc on a line segment AB\" class=\"wp-image-35192\" title=\"Constructing an arc on a line segment AB\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/constructing-an-arc-on-a-line-segment-ab.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/constructing-an-arc-on-a-line-segment-ab-300x179.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Now place the compass at the point of&nbsp; intersection of the arc and the segment and draw another arc such that it cuts the first arc. <em>(We did this to construct a 60 degree angle. All sides of an equilateral angle are equal and each angle measures 60 degrees. Thus, we kept the same radius when drawing bothe the arcs.)<\/em><\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"370\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/constructing-a-60-degree-angle.png\" alt=\"Constructing a 60 degree angle\u00a0\" class=\"wp-image-35193\" title=\"Constructing a 60 degree angle\u00a0\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/constructing-a-60-degree-angle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/constructing-a-60-degree-angle-300x179.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Next, bisect the 60 degree angle to get a 30 degree angle. Use the two intersection points and draw two arcs that meet each other as shown below.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"370\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/bisecting-a-60-degree-angle.png\" alt=\"Bisecting a 60 degree angle\" class=\"wp-image-35194\" title=\"Bisecting a 60 degree angle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/bisecting-a-60-degree-angle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/bisecting-a-60-degree-angle-300x179.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Join the intersection point and the endpoint A.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"370\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/constructing-a-30-degree-angle.png\" alt=\"Constructing a 30 degree angle\" class=\"wp-image-35195\" title=\"Constructing a 30 degree angle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/constructing-a-30-degree-angle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/constructing-a-30-degree-angle-300x179.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Now, repeat the same steps using the endpoint B to consider a similar 30 degree angle.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>Draw a line extending from endpoint B towards the point of interaction.&nbsp;<\/p>\n\n\n\n<p>Join the points where the arcs intersect with the endpoints of the base to form an isosceles triangle. Name the new intersection point as C.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"370\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/steps-for-construction-of-an-isosceles-obtuse-triangle.png\" alt=\"Steps for construction of an isosceles obtuse triangle\" class=\"wp-image-35196\" title=\"Steps for construction of an isosceles obtuse triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/steps-for-construction-of-an-isosceles-obtuse-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/steps-for-construction-of-an-isosceles-obtuse-triangle-300x179.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Measure the angle C using a protractor, it will be 120 degrees, an obtuse angle.<\/li>\n<\/ul>\n\n\n\n<p>Note: Do not change the angle of the compass, the distance between the pointer and pencil throughout your construction.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"370\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/construction-of-an-isosceles-obtuse-angle.png\" alt=\"Construction of an isosceles obtuse angle\" class=\"wp-image-35197\" title=\"Construction of an isosceles obtuse angle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/construction-of-an-isosceles-obtuse-angle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/construction-of-an-isosceles-obtuse-angle-300x179.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-facts-about-isosceles-obtuse-triangle\">Facts about Isosceles Obtuse Triangle<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>An isosceles obtuse triangle is a type of isosceles triangle whose one <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/interior-angles\">interior angle<\/a> is an obtuse angle.<\/li>\n\n\n\n<li>The side which is opposite the obtuse angle is the longest side of the isosceles obtuse triangle.<\/li>\n\n\n\n<li>A triangle cannot be both an isosceles obtuse triangle and a right triangle because it contains an obtuse angle.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about the definitions and important formulas related to obtuse isosceles triangles. Let us now navigate through the numerical section of the article, which covers solved examples and MCQ practice problems.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-solved-examples-on-isosceles-obtuse-triangle\">Solved Examples on Isosceles Obtuse Triangle<\/h2>\n\n\n\n<p><strong>Example 1: If one of the base angles of an isosceles obtuse triangle measures 40<\/strong>\u00b0<strong>, find the remaining angles.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Both base angles are equal in an isosceles triangle.<\/p>\n\n\n\n<p>Thus, the other base angle will also be 40\u00b0.&nbsp;<\/p>\n\n\n\n<p>The total of all angles in a triangle is 180 degrees. Let the measure of the obtuse angle be x degrees.<\/p>\n\n\n\n<p>40\u00b0 + 40\u00b0 + x = 180\u00b0<\/p>\n\n\n\n<p>80\u00b0 + x = 180\u00b0<\/p>\n\n\n\n<p>x = 180\u00b0 \u2013 100\u00b0<\/p>\n\n\n\n<p>x = 100\u00b0<\/p>\n\n\n\n<p>Therefore, the other base angle is 40\u00b0and the obtuse angle is 100\u00b0.<\/p>\n\n\n\n<p><strong>Example 2: An isosceles obtuse triangle has equal sides of 6 units and a base of 8 units. Calculate the height of the triangle.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>The length of equal sides (a) = 6 units<\/p>\n\n\n\n<p>The length of the base (b) = 8 units<\/p>\n\n\n\n<p>For calculating the height of the triangle, we will use the formula:<\/p>\n\n\n\n<p>h $= \\frac{1}{2} \\sqrt{4a^{2} \u2212 b^{2}}$<\/p>\n\n\n\n<p>On substituting the values of a and b into the formula:<\/p>\n\n\n\n<p>h $= \\frac{1}{2} \\sqrt{4(6)^{2} \u2212 (8)^{2}}$<\/p>\n\n\n\n<p>h $= \\frac{1}{2}\\sqrt{80}$<\/p>\n\n\n\n<p>h $= \\frac{1}{2} \\times 8.94$ (approximately)<\/p>\n\n\n\n<p>h = 4.47 units (approximately)<\/p>\n\n\n\n<p><strong>Example 3: The lengths of the sides of an isosceles obtuse triangle are as follows:<\/strong><\/p>\n\n\n\n<p><strong>a = 7 units, b = 7 units, c = 10 units.<\/strong><\/p>\n\n\n\n<p><strong>Use the Heron\u2019s formula to calculate the area of an isosceles obtuse triangle.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Heron&#8217;s formula to find the area of the triangle is given by<\/p>\n\n\n\n<p>A $= \\sqrt{s(s \u2212 a)(s \u2212 b)(s \u2212 c)}$<\/p>\n\n\n\n<p>The semiperimeter \u201cs\u201d of the triangle is given by<\/p>\n\n\n\n<p>$s = \\frac{a + b + c}{2}$&nbsp;<\/p>\n\n\n\n<p>$s = \\frac{2a+b}{2}$ (two sides are equal.)<\/p>\n\n\n\n<p>$s = \\frac{(2(7) + 10)}{2}$&nbsp;<\/p>\n\n\n\n<p>s = 12 units<\/p>\n\n\n\n<p>The area is calculated as<\/p>\n\n\n\n<p>A $= \\sqrt{12(12 \u2212 7)(12 \u2212 7)(12 \u2212 10)}$<\/p>\n\n\n\n<p>A $= \\sqrt{(12 \\times 5 \\times 5 \\times 2)}$<\/p>\n\n\n\n<p>A $= \\sqrt{600}$<\/p>\n\n\n\n<p>A \u2248 24.49 square units<\/p>\n\n\n\n<p><strong>Example 4: If an obtuse isosceles triangle has one side length of 6 units and a base length of 8 units, calculate the perimeter of the triangle.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Equal sides (a) = 6 units<\/p>\n\n\n\n<p>Base (b) = 8 units<\/p>\n\n\n\n<p>The other side is also equal to \u2018a\u2019(isosceles property).<\/p>\n\n\n\n<p>The formula for calculating the perimeter of an obtuse isosceles triangle is:<\/p>\n\n\n\n<p>P = 2a + b<\/p>\n\n\n\n<p>Putting the values in the formula, we get<\/p>\n\n\n\n<p>P = 2(6) + 8<\/p>\n\n\n\n<p>P = 12 + 8<\/p>\n\n\n\n<p>P = 20 units<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-practice-problems-on-isosceles-obtuse-triangle\">Practice Problems on Isosceles Obtuse Triangle<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Isosceles Obtuse Triangle \u2013 Definition, Formulas, Examples, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">How many equal sides does an isosceles obtuse triangle have?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Two equal sides<\/div><div class=\"spq_answer_block\" data-value=\"1\">Three equal sides<\/div><div class=\"spq_answer_block\" data-value=\"2\">Four equal sides<\/div><div class=\"spq_answer_block\" data-value=\"3\">No equal sides<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Two equal sides<br\/>There are two equal sides in an isosceles triangle.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">How many obtuse angles are there in an isosceles obtuse triangle?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1<\/div><div class=\"spq_answer_block\" data-value=\"1\">2<\/div><div class=\"spq_answer_block\" data-value=\"2\">3<\/div><div class=\"spq_answer_block\" data-value=\"3\">4<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 1<br\/>In an isosceles obtuse triangle, there is one obtuse angle.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">In an isosceles obtuse triangle, one interior angle measures 20\u00b0. What is the measure of the obtuse angle?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">20\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"1\">160\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"2\">150\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"3\">140\u00b0<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 140\u00b0<br\/>There are two equal acute angles and one obtuse angle in an isosceles obtuse triangle.<br>\r\nThus, 20\u00b0 + 20\u00b0 + obtuse angle = 180\u00b0<br>\r\nObtuse angle = 140\u00b0<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Identify the isosceles obtuse triangle using the measurement of three interior angles.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">50\u00b0, 50\u00b0, 80\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"1\">45\u00b0, 45\u00b0, 90\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"2\">35\u00b0, 35\u00b0, 110\u00b0<\/div><div class=\"spq_answer_block\" data-value=\"3\">30\u00b0, 50\u00b0, 100\u00b0<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 35\u00b0, 35\u00b0, 110\u00b0<br\/>We need to look for a combination with two acute angles that are equal and one obtuse angle.<br>\r\nThus, the combination of 35\u00b0, 35\u00b0, 110\u00b0 represents an isosceles obtuse triangle.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": 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isosceles obtuse triangle?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"In an isosceles obtuse triangle, there is one obtuse angle.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In an isosceles obtuse triangle, there is one obtuse angle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In an isosceles obtuse triangle, there is one obtuse angle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In an isosceles obtuse triangle, there is one obtuse angle.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"1\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"In an isosceles obtuse triangle, there is one obtuse angle.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"In an isosceles obtuse triangle, there is one obtuse angle.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"In an isosceles obtuse triangle, one interior angle measures 20\u00b0. What is the measure of the obtuse angle?\",\n                    \"text\": \"In an isosceles obtuse triangle, one interior angle measures 20\u00b0. What is the measure of the obtuse angle?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"There are two equal acute angles and one obtuse angle in an isosceles obtuse triangle.<br>\r\nThus, 20\u00b0 + 20\u00b0 + obtuse angle = 180\u00b0<br>\r\nObtuse angle = 140\u00b0\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"20\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"There are two equal acute angles and one obtuse angle in an isosceles obtuse triangle.<br>\r\nThus, 20\u00b0 + 20\u00b0 + obtuse angle = 180\u00b0<br>\r\nObtuse angle = 140\u00b0\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"160\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"There are two equal acute angles and one obtuse angle in an isosceles obtuse triangle.<br>\r\nThus, 20\u00b0 + 20\u00b0 + obtuse angle = 180\u00b0<br>\r\nObtuse angle = 140\u00b0\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"150\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"There are two equal acute angles and one obtuse angle in an isosceles obtuse triangle.<br>\r\nThus, 20\u00b0 + 20\u00b0 + obtuse angle = 180\u00b0<br>\r\nObtuse angle = 140\u00b0\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"140\u00b0\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"There are two equal acute angles and one obtuse angle in an isosceles obtuse triangle.<br>\r\nThus, 20\u00b0 + 20\u00b0 + obtuse angle = 180\u00b0<br>\r\nObtuse angle = 140\u00b0\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"There are two equal acute angles and one obtuse angle in an isosceles obtuse triangle.<br>\r\nThus, 20\u00b0 + 20\u00b0 + obtuse angle = 180\u00b0<br>\r\nObtuse angle = 140\u00b0\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Identify the isosceles obtuse triangle using the measurement of three interior angles.\",\n                    \"text\": \"Identify the isosceles obtuse triangle using the measurement of three interior angles.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We need to look for a combination with two acute angles that are equal and one obtuse angle.<br>\r\nThus, the combination of 35\u00b0, 35\u00b0, 110\u00b0 represents an isosceles obtuse triangle.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"50\u00b0, 50\u00b0, 80\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We need to look for a combination with two acute angles that are equal and one obtuse angle.<br>\r\nThus, the combination of 35\u00b0, 35\u00b0, 110\u00b0 represents an isosceles obtuse triangle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"45\u00b0, 45\u00b0, 90\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We need to look for a combination with two acute angles that are equal and one obtuse angle.<br>\r\nThus, the combination of 35\u00b0, 35\u00b0, 110\u00b0 represents an isosceles obtuse triangle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"30\u00b0, 50\u00b0, 100\u00b0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We need to look for a combination with two acute angles that are equal and one obtuse angle.<br>\r\nThus, the combination of 35\u00b0, 35\u00b0, 110\u00b0 represents an isosceles obtuse triangle.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"35\u00b0, 35\u00b0, 110\u00b0\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We need to look for a combination with two acute angles that are equal and one obtuse angle.<br>\r\nThus, the combination of 35\u00b0, 35\u00b0, 110\u00b0 represents an isosceles obtuse triangle.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We need to look for a combination with two acute angles that are equal and one obtuse angle.<br>\r\nThus, the combination of 35\u00b0, 35\u00b0, 110\u00b0 represents an isosceles obtuse triangle.\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-frequently-asked-questions-about-isosceles-obtuse-triangle\">Frequently Asked Questions about Isosceles Obtuse Triangle<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-ace0daea-478e-4055-a864-9f9cdc6ea2ee\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-ace0daea-478e-4055-a864-9f9cdc6ea2ee\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ace0daea-478e-4055-a864-9f9cdc6ea2ee\"><strong>How many obtuse angles are there in an obtuse isosceles triangle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-ace0daea-478e-4055-a864-9f9cdc6ea2ee\">\n\n<p>There is just one obtuse angle in an obtuse isosceles triangle.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-ace0daea-478e-4055-a864-9f9cdc6ea2ee\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ace0daea-478e-4055-a864-9f9cdc6ea2ee\"><strong>Can an isosceles obtuse triangle be a right triangle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-ace0daea-478e-4055-a864-9f9cdc6ea2ee\">\n\n<p>No, an isosceles obtuse triangle can&#8217;t be a right triangle. An isosceles obtuse triangle has an obtuse angle which is more than 90 degrees.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-ace0daea-478e-4055-a864-9f9cdc6ea2ee\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ace0daea-478e-4055-a864-9f9cdc6ea2ee\"><strong>How to find a missing angle in an obtuse isosceles triangle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-ace0daea-478e-4055-a864-9f9cdc6ea2ee\">\n\n<p>To determine the value of the missing angle, simply subtract the sum of the two given angles from 180 degrees. This will give you the measurement of the angle that is not known.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-ace0daea-478e-4055-a864-9f9cdc6ea2ee\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ace0daea-478e-4055-a864-9f9cdc6ea2ee\"><strong>Is an isosceles obtuse triangle equilateral?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-ace0daea-478e-4055-a864-9f9cdc6ea2ee\">\n\n<p>No, it is not possible for an isosceles obtuse triangle to be an <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/equilateral-triangle\">equilateral triangle<\/a>. An equilateral triangle has all three equal measuring angles, i.e., 60 degrees. It is not possible for an obtuse triangle to have 60 degrees angles.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-ace0daea-478e-4055-a864-9f9cdc6ea2ee\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ace0daea-478e-4055-a864-9f9cdc6ea2ee\"><strong>What are the types of isosceles triangles?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-ace0daea-478e-4055-a864-9f9cdc6ea2ee\">\n\n<p>1) Acute isosceles triangle, 2) Obtuse isosceles triangle, and 3) Right isosceles triangles.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-5-ace0daea-478e-4055-a864-9f9cdc6ea2ee\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ace0daea-478e-4055-a864-9f9cdc6ea2ee\"><strong>What does an obtuse triangle look like?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-5-ace0daea-478e-4055-a864-9f9cdc6ea2ee\">\n\n<p>In an obtuse triangle, there is one obtuse angle and two acute angles. The side opposite to the obtuse angle is the longest side of the triangle.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is an Isosceles Obtuse Triangle in Math? An isosceles obtuse triangle is a triangle in which one interior angle is an obtuse angle and the remaining two angles are equal and acute. An isosceles triangle is a triangle which has two equal sides and the angles opposite to the equal sides are also equal. &#8230; <a title=\"Isosceles Obtuse Triangle \u2013 Definition, Formulas, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/isosceles-obtuse-triangle\" aria-label=\"More on Isosceles Obtuse Triangle \u2013 Definition, Formulas, Examples, FAQs\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-35170","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/35170","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=35170"}],"version-history":[{"count":11,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/35170\/revisions"}],"predecessor-version":[{"id":42300,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/35170\/revisions\/42300"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=35170"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=35170"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=35170"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}