{"id":188105,"date":"2025-02-06T10:41:02","date_gmt":"2025-02-06T10:41:02","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=188105"},"modified":"2025-02-06T10:41:03","modified_gmt":"2025-02-06T10:41:03","slug":"solve-for-x-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/06\/solve-for-x-3\/","title":{"rendered":"Solve for x"},"content":{"rendered":"\n<p>Solve for x. Round to the nearest tenth, if necessary. S 27 18\u00b0 U T \u0445<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/02\/image-78.png\" alt=\"\" class=\"wp-image-188106\"\/><\/figure>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To solve for ( x ) in the given triangle with sides 27 and 18\u00b0 and an unknown side ( x ), we can utilize trigonometric principles. iven that one side and an adjacent angle are known, the Law of Cosines is appropriate for this scenario.<br><strong>Understanding the Law of Cosines:<\/strong><\/p>\n\n\n\n<p>he Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.t is expressed as:<br>[ c^2 = a^2 + b^2 &#8211; 2ab \\cdot \\cos(C) ]<br>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( c ) is the side opposite angle ( C ),- ( a ) and ( b ) are the other two sides,- ( C ) is the included angle between sides ( a ) and ( b ).<br><strong>Applying the Law of Cosines:<\/strong><\/li>\n<\/ul>\n\n\n\n<p>n our case, we have:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Side ( a = 27 )- Angle ( C = 18^\\circ )- Side ( b = x ) (the unknown side)<br>e can rearrange the Law of Cosines to solve for ( x ):<br>[ x^2 = 27^2 + x^2 &#8211; 2 \\times 27 \\times x \\times \\cos(18^\\circ) ]<br>implifying the equation:<br>[ x^2 = 729 + x^2 &#8211; 2 \\times 27 \\times x \\times \\cos(18^\\circ) ]<br>ubtracting ( x^2 ) from both sides:<br>[ 0 = 729 &#8211; 2 \\times 27 \\times x \\times \\cos(18^\\circ) ]<br>olving for ( x ):<br>[ x = \\frac{729}{2 \\times 27 \\times \\cos(18^\\circ)} ]<br>alculating the cosine of 18\u00b0:<br>[ \\cos(18^\\circ) \\approx 0.95106 ]<br>ubstituting this value:<br>[ x = \\frac{729}{2 \\times 27 \\times 0.95106} ]<br>[ x \\approx \\frac{729}{51.45156} ]<br>[ x \\approx 14.2 ]<br><strong>Conclusion:<\/strong><\/li>\n<\/ul>\n\n\n\n<p>he length of side ( x ) is approximately 14.2 units.<br>his calculation demonstrates how the Law of Cosines can be applied to determine an unknown side in a triangle when two sides and the included angle are known.<br>or further practice and to explore more complex triangle problems, you might find the Triangle Calculator tool helpful.\ue200cite\ue202turn0search0\ue201<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solve for x. Round to the nearest tenth, if necessary. S 27 18\u00b0 U T \u0445 The Correct Answer and Explanation is : To solve for ( x ) in the given triangle with sides 27 and 18\u00b0 and an unknown side ( x ), we can utilize trigonometric principles. iven that one side and [&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-188105","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188105","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=188105"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188105\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=188105"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=188105"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=188105"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}