{"id":233671,"date":"2025-06-13T10:03:08","date_gmt":"2025-06-13T10:03:08","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=233671"},"modified":"2025-06-13T10:03:11","modified_gmt":"2025-06-13T10:03:11","slug":"what-is-cos-30-60-2-1-90-30","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/13\/what-is-cos-30-60-2-1-90-30\/","title":{"rendered":"What is cos 30\u00b0? 60\u00b0 2 1 90\u00b0 30\u00b0"},"content":{"rendered":"\n<p>What is cos 30\u00b0? 60\u00b0 2 1 90\u00b0 30\u00b0 ?3 A.<\/p>\n\n\n\n<p>B.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/image-435.png\" alt=\"\" class=\"wp-image-233672\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>C. \u221a3 \/ 2<\/strong><\/p>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<p>To determine the value of cos 30\u00b0, we can use the principles of trigonometry as applied to a right-angled triangle. The mnemonic SOH CAH TOA is a helpful tool for remembering the trigonometric ratios:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>SOH<\/strong>:\u00a0<strong>S<\/strong>ine =\u00a0<strong>O<\/strong>pposite \/\u00a0<strong>H<\/strong>ypotenuse<\/li>\n\n\n\n<li><strong>CAH<\/strong>:\u00a0<strong>C<\/strong>osine =\u00a0<strong>A<\/strong>djacent \/\u00a0<strong>H<\/strong>ypotenuse<\/li>\n\n\n\n<li><strong>TOA<\/strong>:\u00a0<strong>T<\/strong>angent =\u00a0<strong>O<\/strong>pposite \/\u00a0<strong>A<\/strong>djacent<\/li>\n<\/ul>\n\n\n\n<p>The problem provides a 30-60-90 right-angled triangle with its side lengths clearly labeled. To find the cosine of the 30\u00b0 angle, we must first identify the sides of the triangle relative to this specific angle.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Hypotenuse:<\/strong>\u00a0This is always the longest side of a right-angled triangle and is directly opposite the 90\u00b0 angle. In the given triangle, the hypotenuse has a length of\u00a0<strong>2<\/strong>.<\/li>\n\n\n\n<li><strong>Adjacent Side:<\/strong>\u00a0This is the side that is next to the 30\u00b0 angle, but is not the hypotenuse. For the 30\u00b0 angle, the adjacent side has a length of\u00a0<strong>\u221a3<\/strong>.<\/li>\n\n\n\n<li><strong>Opposite Side:<\/strong>\u00a0This is the side directly across from the 30\u00b0 angle. In this case, the opposite side has a length of\u00a0<strong>1<\/strong>.<\/li>\n<\/ol>\n\n\n\n<p>Now, we apply the &#8220;CAH&#8221; formula for cosine:<\/p>\n\n\n\n<p>Cosine = Adjacent \/ Hypotenuse<\/p>\n\n\n\n<p>Substituting the values we identified from the triangle:<\/p>\n\n\n\n<p>cos 30\u00b0 = (Length of Adjacent Side) \/ (Length of Hypotenuse)<br>cos 30\u00b0 = \u221a3 \/ 2<\/p>\n\n\n\n<p>Therefore, the value of cos 30\u00b0 is \u221a3 \/ 2. This corresponds to option C. This is a fundamental value in trigonometry, derived from the properties of a 30-60-90 special right triangle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-299.jpeg\" alt=\"\" class=\"wp-image-233673\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>What is cos 30\u00b0? 60\u00b0 2 1 90\u00b0 30\u00b0 ?3 A. B. The Correct Answer and Explanation is: C. \u221a3 \/ 2 Explanation: To determine the value of cos 30\u00b0, we can use the principles of trigonometry as applied to a right-angled triangle. The mnemonic SOH CAH TOA is a helpful tool for remembering the [&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-233671","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233671","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=233671"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233671\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233671"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233671"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233671"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}