{"id":256725,"date":"2025-07-16T12:47:08","date_gmt":"2025-07-16T12:47:08","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=256725"},"modified":"2025-07-16T12:48:41","modified_gmt":"2025-07-16T12:48:41","slug":"given-a-4-c-3-and-angle-b-100-degrees-find-the-measure-of-angle-c-to-the-nearest-degree","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/16\/given-a-4-c-3-and-angle-b-100-degrees-find-the-measure-of-angle-c-to-the-nearest-degree\/","title":{"rendered":"Given a = 4, c = 3 and angle B = 100 degrees, find the measure of angle C to the nearest degree."},"content":{"rendered":"\n

Given a = 4, c = 3 and angle B = 100 degrees, find the measure of angle C to the nearest degree.<\/p>\n\n\n\n

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

Correct answer:<\/strong>
Angle C \u2248 33\u00b0<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation<\/strong><\/p>\n\n\n\n

To find the measure of angle C in a triangle where side a = 4<\/strong>, side c = 3<\/strong>, and angle B = 100\u00b0<\/strong>, we can apply the Law of Sines<\/strong>. This law relates the sides and angles of any triangle using the formula: asin\u2061A=bsin\u2061B=csin\u2061C\\frac{a}{\\sin A} = \\frac{b}{\\sin B} = \\frac{c}{\\sin C}sinAa\u200b=sinBb\u200b=sinCc\u200b<\/p>\n\n\n\n

In this problem, we are given:<\/p>\n\n\n\n

    \n
  • side a = 4<\/strong><\/li>\n\n\n\n
  • side c = 3<\/strong><\/li>\n\n\n\n
  • angle B = 100\u00b0<\/strong><\/li>\n<\/ul>\n\n\n\n

    We want to find angle C<\/strong>.<\/p>\n\n\n\n

    Step 1: Use the Law of Sines<\/h3>\n\n\n\n

    We will write: asin\u2061A=csin\u2061C\\frac{a}{\\sin A} = \\frac{c}{\\sin C}sinAa\u200b=sinCc\u200b<\/p>\n\n\n\n

    But we do not know angle A yet. We can instead use this variation: 4sin\u2061A=3sin\u2061Candangle B = 100\u00b0\\frac{4}{\\sin A} = \\frac{3}{\\sin C} \\quad \\text{and} \\quad \\text{angle B = 100\u00b0}sinA4\u200b=sinC3\u200bandangle B = 100\u00b0<\/p>\n\n\n\n

    Since the sum of angles in any triangle is 180\u00b0, we can express angle A as: A=180\u00b0\u2212B\u2212C=80\u00b0\u2212CA = 180\u00b0 – B – C = 80\u00b0 – CA=180\u00b0\u2212B\u2212C=80\u00b0\u2212C<\/p>\n\n\n\n

    Now we substitute into the Law of Sines: 4sin\u2061(80\u00b0\u2212C)=3sin\u2061C\\frac{4}{\\sin (80\u00b0 – C)} = \\frac{3}{\\sin C}sin(80\u00b0\u2212C)4\u200b=sinC3\u200b<\/p>\n\n\n\n

    This equation is difficult to solve algebraically, so instead, we try a numerical approach by guessing values of angle C and refining our guess.<\/p>\n\n\n\n

    Try C = 33\u00b0<\/strong>:<\/p>\n\n\n\n

    Then A = 180 – 100 – 33 = 47\u00b0<\/strong><\/p>\n\n\n\n

    Now apply Law of Sines: asin\u2061A=csin\u2061C\u21d24sin\u206147\u00b0\u22485.478and3sin\u206133\u00b0\u22485.507\\frac{a}{\\sin A} = \\frac{c}{\\sin C} \\quad \\Rightarrow \\quad \\frac{4}{\\sin 47\u00b0} \\approx 5.478 \\quad \\text{and} \\quad \\frac{3}{\\sin 33\u00b0} \\approx 5.507sinAa\u200b=sinCc\u200b\u21d2sin47\u00b04\u200b\u22485.478andsin33\u00b03\u200b\u22485.507<\/p>\n\n\n\n

    Very close match. So angle C is approximately 33\u00b0<\/strong>.<\/p>\n\n\n\n

    This method shows how we can find missing angles using known sides and one angle, applying the Law of Sines and using the angle sum property of triangles.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    Given a = 4, c = 3 and angle B = 100 degrees, find the measure of angle C to the nearest degree. The Correct Answer and Explanation is: Correct answer:Angle C \u2248 33\u00b0 Explanation To find the measure of angle C in a triangle where side a = 4, side c = 3, and […]<\/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-256725","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/256725","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=256725"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/256725\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=256725"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=256725"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=256725"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}