{"id":265631,"date":"2025-07-22T07:58:00","date_gmt":"2025-07-22T07:58:00","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=265631"},"modified":"2025-07-22T07:58:02","modified_gmt":"2025-07-22T07:58:02","slug":"which-equation-can-be-used-to-solve-for-c-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/22\/which-equation-can-be-used-to-solve-for-c-2\/","title":{"rendered":"Which equation can be used to solve for c"},"content":{"rendered":"\n<p>Which equation can be used to solve for c? Triangle A B C is shown. Angle A C B is 90 degrees and angle A B C is 35 degrees. The length of C B is 5 inches, the length of A C is b, and the length of B A is c.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve for ccc in triangle ABC, where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2220ACB=90\u2218\\angle ACB = 90^\\circ\u2220ACB=90\u2218 (a right triangle),<\/li>\n\n\n\n<li>\u2220ABC=35\u2218\\angle ABC = 35^\\circ\u2220ABC=35\u2218,<\/li>\n\n\n\n<li>CB=5CB = 5CB=5 inches (the length of the side opposite angle A),<\/li>\n\n\n\n<li>AC=bAC = bAC=b inches (the length of the side opposite angle B),<\/li>\n\n\n\n<li>AB=cAB = cAB=c inches (the hypotenuse).<\/li>\n<\/ul>\n\n\n\n<p>We can apply <strong>trigonometric functions<\/strong> like sine, cosine, and Pythagoras\u2019 theorem to solve for ccc.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Use the cosine function.<\/h3>\n\n\n\n<p>Since \u2220ABC=35\u2218\\angle ABC = 35^\\circ\u2220ABC=35\u2218 and ABABAB is the hypotenuse of the right triangle, we can use the <strong>cosine function<\/strong> to relate ccc to the sides:cos\u2061(\u2220ABC)=adjacenthypotenuse=ACAB=bc\\cos(\\angle ABC) = \\frac{\\text{adjacent}}{\\text{hypotenuse}} = \\frac{AC}{AB} = \\frac{b}{c}cos(\u2220ABC)=hypotenuseadjacent\u200b=ABAC\u200b=cb\u200b<\/p>\n\n\n\n<p>This gives us the equation:cos\u2061(35\u2218)=bc\\cos(35^\\circ) = \\frac{b}{c}cos(35\u2218)=cb\u200b<\/p>\n\n\n\n<p>Rearranging to solve for ccc, we get:c=bcos\u2061(35\u2218)c = \\frac{b}{\\cos(35^\\circ)}c=cos(35\u2218)b\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Use the Pythagorean theorem for verification.<\/h3>\n\n\n\n<p>Since triangle ABC is a right triangle, you can also use the Pythagorean theorem to find the relationship between the sides:AB2=AC2+BC2AB^2 = AC^2 + BC^2AB2=AC2+BC2<\/p>\n\n\n\n<p>Substituting the known values, we get:c2=b2+52c^2 = b^2 + 5^2c2=b2+52<\/p>\n\n\n\n<p>So, the second equation you can use is:c=b2+25c = \\sqrt{b^2 + 25}c=b2+25\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>You can solve for ccc using either the equation c=bcos\u2061(35\u2218)c = \\frac{b}{\\cos(35^\\circ)}c=cos(35\u2218)b\u200b (from trigonometry) or c=b2+25c = \\sqrt{b^2 + 25}c=b2+25\u200b (from the Pythagorean theorem). Each approach gives you a way to express ccc in terms of bbb, depending on the available information in the problem.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1491.jpeg\" alt=\"\" class=\"wp-image-265637\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Which equation can be used to solve for c? Triangle A B C is shown. Angle A C B is 90 degrees and angle A B C is 35 degrees. The length of C B is 5 inches, the length of A C is b, and the length of B A is c. The Correct [&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-265631","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/265631","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=265631"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/265631\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=265631"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=265631"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=265631"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}