{"id":256720,"date":"2025-07-16T12:45:04","date_gmt":"2025-07-16T12:45:04","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=256720"},"modified":"2025-07-16T12:45:08","modified_gmt":"2025-07-16T12:45:08","slug":"determine-the-measure-of-the-angle-c-to-the-nearest-degree","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/16\/determine-the-measure-of-the-angle-c-to-the-nearest-degree\/","title":{"rendered":"Determine the measure of the angle C to the nearest degree."},"content":{"rendered":"\n<p>Determine the measure of the angle C to the nearest degree. 11 cm 7 cm 38\u00b0 C<\/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\/image-481.png\" alt=\"\" class=\"wp-image-256721\"\/><\/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>The correct measure of angle C to the nearest degree is&nbsp;<strong>105\u00b0<\/strong>.<\/p>\n\n\n\n<p>Here is a step-by-step explanation of how to find the measure of angle C:<\/p>\n\n\n\n<p><strong>1. Identify the Given Information<\/strong><br>From the provided image of triangle ABC, we have the following known values:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The length of the side opposite angle B (side AC) is b = 7 cm.<\/li>\n\n\n\n<li>The measure of angle B is 38\u00b0.<\/li>\n\n\n\n<li>The length of the side opposite angle C (side AB) is c = 11 cm.<br>We need to determine the measure of angle C.<\/li>\n<\/ul>\n\n\n\n<p><strong>2. Choose the Appropriate Trigonometric Law<\/strong><br>This problem involves a triangle where we know two sides and a non-included angle (SSA configuration). The Law of Sines is the appropriate tool for this situation. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides. The formula is:<br>a\/sin(A) = b\/sin(B) = c\/sin(C)<\/p>\n\n\n\n<p><strong>3. Set Up the Equation<\/strong><br>Using the parts of the Law of Sines that involve our known and unknown values, we can set up the following proportion:<br>b \/ sin(B) = c \/ sin(C)<\/p>\n\n\n\n<p>Substitute the given values into the equation:<br>7 \/ sin(38\u00b0) = 11 \/ sin(C)<\/p>\n\n\n\n<p><strong>4. Solve for Angle C<\/strong><br>To solve for angle C, we first need to isolate sin(C). We can do this by cross-multiplying:<br>7 * sin(C) = 11 * sin(38\u00b0)<\/p>\n\n\n\n<p>Next, divide both sides by 7:<br>sin(C) = (11 * sin(38\u00b0)) \/ 7<\/p>\n\n\n\n<p>Now, use a calculator to find the value of sin(38\u00b0) and perform the calculation:<br>sin(38\u00b0) \u2248 0.6157<br>sin(C) \u2248 (11 * 0.6157) \/ 7<br>sin(C) \u2248 6.7727 \/ 7<br>sin(C) \u2248 0.9675<\/p>\n\n\n\n<p>To find the angle C, we take the inverse sine (arcsin) of this value:<br>C = arcsin(0.9675)<br>C \u2248 75.4\u00b0<\/p>\n\n\n\n<p><strong>5. Consider the Ambiguous Case (SSA)<\/strong><br>The Side-Side-Angle (SSA) case is known as the ambiguous case because it can sometimes result in two possible triangles. When sin(C) is calculated, there are two possible angles between 0\u00b0 and 180\u00b0: an acute angle (C\u2081) and an obtuse angle (C\u2082 = 180\u00b0 &#8211; C\u2081).<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The first possible angle is C\u2081 \u2248 75.4\u00b0.<\/li>\n\n\n\n<li>The second possible angle is C\u2082 = 180\u00b0 &#8211; 75.4\u00b0 = 104.6\u00b0.<\/li>\n<\/ul>\n\n\n\n<p>To determine which angle is correct, we look at the diagram. The drawing clearly shows that angle C is an obtuse angle, meaning it is greater than 90\u00b0. Therefore, we must choose the obtuse solution.<\/p>\n\n\n\n<p><strong>6. Final Calculation and Rounding<\/strong><br>The correct measure for angle C is approximately 104.6\u00b0. The problem asks for the answer to be rounded to the nearest degree.<br>Rounding 104.6\u00b0 to the nearest degree gives us&nbsp;<strong>105\u00b0<\/strong>.<\/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-banner6-676.jpeg\" alt=\"\" class=\"wp-image-256722\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Determine the measure of the angle C to the nearest degree. 11 cm 7 cm 38\u00b0 C The Correct Answer and Explanation is: The correct measure of angle C to the nearest degree is&nbsp;105\u00b0. Here is a step-by-step explanation of how to find the measure of angle C: 1. Identify the Given InformationFrom the provided [&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-256720","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/256720","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=256720"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/256720\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=256720"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=256720"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=256720"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}