{"id":5750,"date":"2022-06-29T11:27:19","date_gmt":"2022-06-29T11:27:19","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=5750"},"modified":"2024-02-05T11:25:14","modified_gmt":"2024-02-05T11:25:14","slug":"30-60-90-triangle-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/30-60-90-triangle","title":{"rendered":"30 60 90 Triangle &#8211; Definition with Examples"},"content":{"rendered":"\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\"><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-bc3b944a-8359-4cfe-bc9a-f3d0a60b4f19\" 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\/30-60-90-triangle#0-what-is-a-%E2%80%9C30-60-90%E2%80%9D-triangle>What Is a \u201c30-60-90\u201d Triangle?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/30-60-90-triangle#1-30-60-90-triangle-rule>30-60-90 Triangle Rule<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/30-60-90-triangle#2-area-of-the-30-60-90-triangle>Area of the 30-60-90 Triangle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/30-60-90-triangle#4-solved-examples>Solved Examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/30-60-90-triangle#5-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/30-60-90-triangle#6-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<p class=\"eplus-wrapper\">A three sided polygon is known as a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/triangle\" title=\"\">triangle<\/a>. A triangle has 3 sides, 3 vertices and 3 angles. There are different ways in which we can categorize the triangles. On the basis of sides, a triangle can be scalene, isosceles, or equilateral. However, in some cases, a triangle may possess unique properties. Such triangles are called special triangles. One such special triangle is the 30\u00b0\u201360\u00b0\u201390\u00b0 triangles.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-a-%E2%80%9C30-60-90%E2%80%9D-triangle\">What Is a \u201c30-60-90\u201d Triangle?<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"326\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/30-60-90-Triangle-1.png\" alt=\"30\u00b0\u201360\u00b0\u201390\u00b0 triangles\" class=\"wp-image-5759\" title=\"30\u00b0\u201360\u00b0\u201390\u00b0 triangles\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/30-60-90-Triangle-1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/30-60-90-Triangle-1-300x158.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">A special right triangle with angles 30\u00b0, 60\u00b0, and 90\u00b0 is called a 30-60-90 triangle. The angles of a 30-60-90 triangle are in the ratio 1 : 2 : 3. Since 30\u00b0 is the smallest angle in the triangle, the side opposite to the 30\u00b0 angle is always the smallest (shortest leg). The side opposite to the 60\u00b0 angle is the longer leg, and finally, the side opposite to the 90\u00b0 angle is the largest side of the right triangle, also known as the hypotenuse.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since the 30-60-90 triangle is a special triangle, the side lengths of the 30-60-90 triangle are in a constant relationship.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"308\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/30-60-90-Triangle-2.png\" alt=\"Side length ratio of a 30-60-90 triangle\" class=\"wp-image-5760\" title=\"Side length ratio of a 30-60-90 triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/30-60-90-Triangle-2.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/30-60-90-Triangle-2-300x149.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">From the figure above, we can make the following observations about the side length ratio of a 30-60-90 triangle:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The side opposite the 30\u00b0 angle: PQ = a<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The side opposite the 60\u00b0 angle: QR = a\u221a3<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The side opposite the 90\u00b0 angle: PR = 2a<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">The sides of a 30-60-90 triangle are always in the ratio of <strong>1 : \u221a3 : 2<\/strong>.<strong>&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">For example:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, in triangle PQR,&nbsp;<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The side opposite to the 30\u00b0 angle is PQ = a = 5 units&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The side opposite to the 60\u00b0 angle is QR = a\u221a3 = 5\u221a3 units<\/li>\n\n\n\n<li class=\"eplus-wrapper\">The side opposite to the 90\u00b0 angle is PQ = 2a = 10 units<\/li>\n<\/ul>\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-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            }\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 eplus-wrapper\" id=\"1-30-60-90-triangle-rule\">30-60-90 Triangle Rule<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In a 30-60-90 triangle, we can find the measure of any of the three sides by knowing the measure of at least one side in the triangle. This is known as the <strong>30-60-90 triangle rule<\/strong>. The following shows how to find the sides of a 30-60-90 triangle using this rule:&nbsp;<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">When the side opposite to 30\u00b0 is given.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"327\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/30-60-90-Triangle-3.png\" alt=\"Side opposite to 30\u00b0\" class=\"wp-image-5761\" title=\"Side opposite to 30\u00b0\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/30-60-90-Triangle-3.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/30-60-90-Triangle-3-300x158.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Consider the side opposite to 30\u00b0 (shortest side), AB to be &#8216;a&#8217;.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The side opposite to 60\u00b0, BC = a\u221a3&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The side opposite to 90\u00b0 (hypotenuse), AC = 2a<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">When the side opposite to 60\u00b0 is given.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"335\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/30-60-90-Triangle-4.png\" alt=\"Side opposite to 60\u00b0\" class=\"wp-image-5762\" title=\"Side opposite to 60\u00b0\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/30-60-90-Triangle-4.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/30-60-90-Triangle-4-300x162.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Consider the side opposite to 60\u00b0, EF to be &#8216;a&#8217;.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The side opposite to 30\u00b0, DE = $\\frac{a}{\\sqrt{3}}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The side opposite to 90\u00b0 (hypotenuse), DF = $\\frac{2a}{\\sqrt{3}}$<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">When hypotenuse is given.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"313\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/30-60-90-Triangle-5.png\" alt=\"Hypotenuse of the triangle\" class=\"wp-image-5763\" title=\"Hypotenuse of the triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/30-60-90-Triangle-5.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/30-60-90-Triangle-5-300x151.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Consider the hypotenuse of the triangle, i.e., PR to be &#8216;a&#8217;.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The side opposite to 30\u00b0, PQ = $\\frac{a}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The side opposite to 60\u00b0, QR = $\\frac{\\sqrt{3}}{2}$a<\/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\/division-by-3-within-30\" 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\/division-by-3-within-30.jpeg\" alt=\"Division by 3 within 30\">\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\/division-by-6-within-60\" 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\/division-by-6-within-60.jpeg\" alt=\"Division by 6 within 60\">\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\/division-by-9-within-90\" 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\/division-by-9-within-90.jpeg\" alt=\"Division by 9 within 90\">\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\/factors-of-30\" 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\/factors-of-30.jpeg\" alt=\"Factors of 30\">\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\/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 eplus-wrapper\" id=\"2-area-of-the-30-60-90-triangle\">Area of the 30-60-90 Triangle<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"315\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/30-60-90-Triangle-6.png\" alt=\"Perpendicular of triangle\" class=\"wp-image-5764\" title=\"Perpendicular of triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/30-60-90-Triangle-6.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/30-60-90-Triangle-6-300x152.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">When the perpendicular is given to be a,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of $\\Delta$DEF = $\\frac{1}{2} \\times base \\times height$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">= $\\frac{1}{2} \\times a \\sqrt{3} \\times a = \\frac{\\sqrt{3}a^{2}}{2}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In this article, we learned about a special triangle, i.e., the 30-60-90 triangle. To read more such informative articles on other concepts, visit our website. We, at <a href=\"https:\/\/www.splashlearn.com\/\" title=\"\">SplashLearn<\/a>, are on a mission to make learning fun and interactive for all students.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-solved-examples\">Solved Examples<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. Find the length of the side BC in the following figure.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"292\" height=\"175\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Solved-Example-1-3.png\" alt=\"Find the length of the side BC\" class=\"wp-image-5766\" title=\"Find the length of the side BC\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Answer: The side opposite to 30\u02da (shortest side), AB = 6 cm<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since the sides of a 30-60-90 triangle are always in the ratio of <strong>1 : \u221a3 : 2.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, the sides of the given triangle are AB = 6 cm, BC = 6\u221a3 cm and AC = 12 cm.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, BC = 6\u221a3 cm<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. Find the length of the hypotenuse in the following figure.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"269\" height=\"191\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Solved-Example-2-2.png\" alt=\"Find the length of the hypotenuse\" class=\"wp-image-5768\" title=\"Find the length of the hypotenuse\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Answer: Side opposite to 60\u02da, QR = a = 8\u221a3 cm&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The hypotenuse of the triangle, i.e., PR = $\\frac{2a}{\\sqrt{3}} = \\frac{2 \u00d7 8\u221a3}{\\sqrt{3}}$ = 16 units.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3.&nbsp; <\/strong><strong>A triangle has sides 3\u221a2, 3\u221a6, and 3\u221a8. Find the angles of this triangle.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Answer: The sides of the triangle are 3\u221a2, 3\u221a6, and 3\u221a8.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let us check whether the sides are of the 30-60-90 triangle.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">On dividing each side of the triangle by 3\u221a2, we get 1, \u221a3, and 2. Therefore, sides of the triangle are 3\u221a2, 3\u221a6, and 3\u221a8, are in the ratio 1: \u221a3: 2.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The sides are following the 30-60-90 triangle rule. So, the angles of the given triangle&nbsp;are 30\u00b0, 60\u00b0, and 90\u00b0.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-practice-problems\">Practice Problems<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">30 60 90 Triangle<\/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\">Which of the following forms a 30-60-90 triangle?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">5, 5\u221a3, 10<\/div><div class=\"spq_answer_block\" data-value=\"1\">5, 5\u221a3, 20<\/div><div class=\"spq_answer_block\" data-value=\"2\">10, 5\u221a3, 10<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of these<\/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: 5, 5\u221a3, 10<br\/>On dividing the ratio 5 : 5\u221a3 : 10 by 5, we get 1 : \u221a3 : 2. It follows the 30-60-90 triangle rule.<\/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\">The hypotenuse of a 30-60-90 triangle as shown below is 20 ft. Find the length of the shortest side of the triangle?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">10 feet<\/div><div class=\"spq_answer_block\" data-value=\"1\">10$\\sqrt{3}$ feet<\/div><div class=\"spq_answer_block\" data-value=\"2\">15<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{10 \\sqrt{3}}{3}$ feet<\/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: 10 feet<br\/>In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shortest side. So, the shortest side of the triangle must be $\\frac{hypotenuse}{2}$ = $\\frac{20}{2}$ = 10 ft<\/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\">What will be the area of the triangle if the base is given to be 4\u221a3 cm?<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Practice-Problem-3.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">4 cm$^{2}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">4$\\sqrt{3}$ cm$^{2}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">8 cm$^{2}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">8$\\sqrt{3}$ cm$^{2}$<\/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: 8$\\sqrt{3}$ cm$^{2}$<br\/>Base is 4\u221a3 cm and perpendicular must be 4 cm. \r\nSo, Area of the triangle = $\\frac{1}{2} \\times 4 \\times 4\u221a3 = 8\u221a3 cm^{2}$<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this Quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"30 60 90 Triangle\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"30 60 90 Triangle\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following forms a 30-60-90 triangle?\",\n                    \"text\": \"Which of the following forms a 30-60-90 triangle?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"On dividing the ratio 5 : 5\u221a3 : 10 by 5, we get 1 : \u221a3 : 2. It follows the 30-60-90 triangle rule.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5, 5\u221a3, 20\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"On dividing the ratio 5 : 5\u221a3 : 10 by 5, we get 1 : \u221a3 : 2. It follows the 30-60-90 triangle rule.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10, 5\u221a3, 10\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"On dividing the ratio 5 : 5\u221a3 : 10 by 5, we get 1 : \u221a3 : 2. It follows the 30-60-90 triangle rule.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of these\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"On dividing the ratio 5 : 5\u221a3 : 10 by 5, we get 1 : \u221a3 : 2. It follows the 30-60-90 triangle rule.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"5, 5\u221a3, 10\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"On dividing the ratio 5 : 5\u221a3 : 10 by 5, we get 1 : \u221a3 : 2. It follows the 30-60-90 triangle rule.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"On dividing the ratio 5 : 5\u221a3 : 10 by 5, we get 1 : \u221a3 : 2. It follows the 30-60-90 triangle rule.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The hypotenuse of a 30-60-90 triangle as shown below is 20 ft. Find the length of the shortest side of the triangle?\",\n                    \"text\": \"The hypotenuse of a 30-60-90 triangle as shown below is 20 ft. Find the length of the shortest side of the triangle?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shortest side. So, the shortest side of the triangle must be $$\\\\frac{hypotenuse}{2}$$ = $$\\\\frac{20}{2}$$ = 10 ft\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10$$\\\\sqrt{3}$$ feet\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shortest side. So, the shortest side of the triangle must be $$\\\\frac{hypotenuse}{2}$$ = $$\\\\frac{20}{2}$$ = 10 ft\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"15\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shortest side. So, the shortest side of the triangle must be $$\\\\frac{hypotenuse}{2}$$ = $$\\\\frac{20}{2}$$ = 10 ft\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{10 \\\\sqrt{3}}{3}$$ feet\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shortest side. So, the shortest side of the triangle must be $$\\\\frac{hypotenuse}{2}$$ = $$\\\\frac{20}{2}$$ = 10 ft\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"10 feet\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shortest side. So, the shortest side of the triangle must be $$\\\\frac{hypotenuse}{2}$$ = $$\\\\frac{20}{2}$$ = 10 ft\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shortest side. So, the shortest side of the triangle must be $$\\\\frac{hypotenuse}{2}$$ = $$\\\\frac{20}{2}$$ = 10 ft\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What will be the area of the triangle if the base is given to be 4\u221a3 cm?\",\n                    \"text\": \"What will be the area of the triangle if the base is given to be 4\u221a3 cm? <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/06\/Practice-Problem-3.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Base is 4\u221a3 cm and perpendicular must be 4 cm. \r\nSo, Area of the triangle = $$\\\\frac{1}{2} \\\\times 4 \\\\times 4\u221a3 = 8\u221a3 cm^{2}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4 cm$$^{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Base is 4\u221a3 cm and perpendicular must be 4 cm. \r\nSo, Area of the triangle = $$\\\\frac{1}{2} \\\\times 4 \\\\times 4\u221a3 = 8\u221a3 cm^{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4$$\\\\sqrt{3}$$ cm$$^{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Base is 4\u221a3 cm and perpendicular must be 4 cm. \r\nSo, Area of the triangle = $$\\\\frac{1}{2} \\\\times 4 \\\\times 4\u221a3 = 8\u221a3 cm^{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"8 cm$$^{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Base is 4\u221a3 cm and perpendicular must be 4 cm. \r\nSo, Area of the triangle = $$\\\\frac{1}{2} \\\\times 4 \\\\times 4\u221a3 = 8\u221a3 cm^{2}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"8$$\\\\sqrt{3}$$ cm$$^{2}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Base is 4\u221a3 cm and perpendicular must be 4 cm. \r\nSo, Area of the triangle = $$\\\\frac{1}{2} \\\\times 4 \\\\times 4\u221a3 = 8\u221a3 cm^{2}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Base is 4\u221a3 cm and perpendicular must be 4 cm. \r\nSo, Area of the triangle = $$\\\\frac{1}{2} \\\\times 4 \\\\times 4\u221a3 = 8\u221a3 cm^{2}$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-2822a8df-5e02-4c2a-ae45-69b51b163b39\" 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-0-2822a8df-5e02-4c2a-ae45-69b51b163b39\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-2822a8df-5e02-4c2a-ae45-69b51b163b39\"><strong>How is the 30-60-90 triangle similar to 45-45-90?<\/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-0-2822a8df-5e02-4c2a-ae45-69b51b163b39\">\n\n<p>These are some similarities between the 30-60-90 triangle and 45-45-90 triangle.&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Both are <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/right-triangle\" title=\"\">right-angle triangles<\/a>.\u00a0<\/li>\n\n\n\n<li>Both follow Pythagorean theorem.<\/li>\n\n\n\n<li>Sum of the interior angles of both are 180 degrees.<\/li>\n<\/ul>\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-1-2822a8df-5e02-4c2a-ae45-69b51b163b39\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-2822a8df-5e02-4c2a-ae45-69b51b163b39\"><strong>What is the perimeter of a 30-60-90 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-1-2822a8df-5e02-4c2a-ae45-69b51b163b39\">\n\n<p>Let the perpendicular be a.&nbsp;<\/p>\n\n\n\n<p>Base = 3a<\/p>\n\n\n\n<p>Hypotenuse = 2a&nbsp;Perimeter = Sum of all the sides = a+3a+2a = a(3+3) units<\/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-2-2822a8df-5e02-4c2a-ae45-69b51b163b39\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-2822a8df-5e02-4c2a-ae45-69b51b163b39\"><strong>Which side is the longer leg of a 30-60-90 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-2-2822a8df-5e02-4c2a-ae45-69b51b163b39\">\n\n<p>The long leg of a 30-60-90 triangle is the one whose length is greater than the shortest leg and less than the hypotenuse. In other words, it is the side opposite the 60 degree angle.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>A three sided polygon is known as a triangle. A triangle has 3 sides, 3 vertices and 3 angles. There are different ways in which we can categorize the triangles. On the basis of sides, a triangle can be scalene, isosceles, or equilateral. However, in some cases, a triangle may possess unique properties. Such triangles &#8230; <a title=\"30 60 90 Triangle &#8211; Definition with Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/30-60-90-triangle\" aria-label=\"More on 30 60 90 Triangle &#8211; Definition with Examples\">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-5750","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\/5750","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=5750"}],"version-history":[{"count":13,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/5750\/revisions"}],"predecessor-version":[{"id":39905,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/5750\/revisions\/39905"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=5750"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=5750"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=5750"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}