{"id":144467,"date":"2024-09-24T17:21:13","date_gmt":"2024-09-24T17:21:13","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=144467"},"modified":"2024-09-24T17:21:16","modified_gmt":"2024-09-24T17:21:16","slug":"find-the-measure-of-side-c","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/09\/24\/find-the-measure-of-side-c\/","title":{"rendered":"Find the measure of side c"},"content":{"rendered":"\n

Find the measure of side c.<\/strong><\/p>\n\n\n\n

8.8<\/strong>
10.3<\/strong>
9.7<\/strong>
8.5<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

To find the measure of side ( c ) in a triangle where the other sides are given, we can use the Law of Cosines, which states:<\/p>\n\n\n\n

[
c^2 = a^2 + b^2 – 2ab \\cdot \\cos(C)
]<\/p>\n\n\n\n

where:<\/p>\n\n\n\n

    \n
  • ( c ) is the side opposite angle ( C ),<\/li>\n\n\n\n
  • ( a ) and ( b ) are the other two sides,<\/li>\n\n\n\n
  • ( C ) is the angle opposite side ( c ).<\/li>\n<\/ul>\n\n\n\n

    Assuming you have the lengths of sides ( a ) and ( b ) (e.g., 8.8 and 10.3) and the angle ( C ) (not specified in your question), you can plug in the values.<\/p>\n\n\n\n

    Let\u2019s assume:<\/p>\n\n\n\n

      \n
    • ( a = 8.8 )<\/li>\n\n\n\n
    • ( b = 10.3 )<\/li>\n\n\n\n
    • ( C = 9.7^\\circ ) (this is a hypothetical value for illustration).<\/li>\n<\/ul>\n\n\n\n
        \n
      1. Calculate ( a^2 ) and ( b^2 )<\/strong>:
        [
        a^2 = 8.8^2 = 77.44
        ]
        [
        b^2 = 10.3^2 = 106.09
        ]<\/li>\n\n\n\n
      2. Calculate ( 2ab \\cdot \\cos(C) )<\/strong>:
        [
        \\cos(9.7^\\circ) \\approx 0.9848 \\quad \\text{(using a calculator)}
        ]
        [
        2ab \\cdot \\cos(C) = 2 \\cdot 8.8 \\cdot 10.3 \\cdot 0.9848 \\approx 181.56
        ]<\/li>\n\n\n\n
      3. Substituting into the Law of Cosines<\/strong>:
        [
        c^2 = 77.44 + 106.09 – 181.56
        ]
        [
        c^2 \\approx 1.97
        ]
        [
        c \\approx \\sqrt{1.97} \\approx 1.4
        ]<\/li>\n<\/ol>\n\n\n\n

        Thus, the measure of side ( c ) is approximately 1.4<\/strong> units.<\/p>\n\n\n\n

        If you can provide the specific angle or clarify the question further, I can refine this calculation accordingly!<\/p>\n","protected":false},"excerpt":{"rendered":"

        Find the measure of side c. 8.810.39.78.5 The Correct Answer and Explanation is : To find the measure of side ( c ) in a triangle where the other sides are given, we can use the Law of Cosines, which states: [c^2 = a^2 + b^2 – 2ab \\cdot \\cos(C)] where: Assuming you have the […]<\/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-144467","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/144467","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=144467"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/144467\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=144467"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=144467"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=144467"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}