{"id":242398,"date":"2025-07-04T07:21:59","date_gmt":"2025-07-04T07:21:59","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=242398"},"modified":"2025-07-04T07:22:00","modified_gmt":"2025-07-04T07:22:00","slug":"the-following-statements-about-30-60-90-triangles-are-true-except","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/04\/the-following-statements-about-30-60-90-triangles-are-true-except\/","title":{"rendered":"The following statements about 30 &#8211; 60 &#8211; 90 triangles are true EXCEPT"},"content":{"rendered":"\n<p>The following statements about 30 &#8211; 60 &#8211; 90 triangles are true EXCEPT: <\/p>\n\n\n\n<p>a. The shorter leg is the hypotenuse or times the longer leg. <\/p>\n\n\n\n<p>b. The longer leg is times the shorter leg. <\/p>\n\n\n\n<p>c. The longer leg is 3 times the shorter leg.<\/p>\n\n\n\n<p> d. The hypotenuse is twice the shorter leg.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer is <strong>c. The longer leg is 3 times the shorter leg<\/strong>.<\/p>\n\n\n\n<p>In a 30-60-90 triangle, the ratio of the lengths of the sides follows a specific pattern derived from the properties of right triangles. Here&#8217;s how it works:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Hypotenuse<\/strong>: The hypotenuse is always <strong>twice the length of the shorter leg<\/strong>. This is a fundamental property of 30-60-90 triangles.<\/li>\n\n\n\n<li><strong>Shorter Leg<\/strong>: The shorter leg is opposite the 30-degree angle and is typically denoted as <strong>x<\/strong>.<\/li>\n\n\n\n<li><strong>Longer Leg<\/strong>: The longer leg is opposite the 60-degree angle and is denoted as <strong>x\u221a3<\/strong>. This leg is longer than the shorter leg but <strong>not<\/strong> three times as long, which is why statement c is false.<\/li>\n<\/ol>\n\n\n\n<p>To summarize, the correct relationships are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>hypotenuse<\/strong> = 2 \u00d7 shorter leg (x).<\/li>\n\n\n\n<li>The <strong>longer leg<\/strong> = shorter leg \u00d7 \u221a3 (x\u221a3).<\/li>\n\n\n\n<li>The <strong>shorter leg<\/strong> is simply <strong>x<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>For example, if the shorter leg (opposite the 30-degree angle) is 5 units, the hypotenuse will be 10 units (5 \u00d7 2), and the longer leg will be 5\u221a3, or approximately 8.66 units (5 \u00d7 \u221a3).<\/p>\n\n\n\n<p>In this case, <strong>the statement that the longer leg is 3 times the shorter leg (c)<\/strong> does not hold true because the ratio of the longer leg to the shorter leg is actually \u221a3, not 3. This means the longest side is not three times as long as the shortest side in a 30-60-90 triangle.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The following statements about 30 &#8211; 60 &#8211; 90 triangles are true EXCEPT: a. The shorter leg is the hypotenuse or times the longer leg. b. The longer leg is times the shorter leg. c. The longer leg is 3 times the shorter leg. d. The hypotenuse is twice the shorter leg. The correct answer [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-242398","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242398","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=242398"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242398\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=242398"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=242398"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=242398"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}