{"id":7631,"date":"2022-09-16T06:26:05","date_gmt":"2022-09-16T06:26:05","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=7631"},"modified":"2022-09-16T06:26:05","modified_gmt":"2022-09-16T06:26:05","slug":"law-of-cosines-cosine-rule","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/09\/16\/law-of-cosines-cosine-rule\/","title":{"rendered":"Law of Cosines \/ Cosine Rule"},"content":{"rendered":"\n<p>In these lessons, we will learn:<\/p>\n\n\n\n<ul><li>the Law of Cosines<\/li><li>how to use the Law of Cosines when given two sides and an included angle<\/li><li>how to use the Law of Cosines when given three sides<\/li><li>how to proof the Law of Cosines<\/li><li>how to solve applications or word problems using the Law of Cosine<\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"law-of-cosines\">Law of Cosines<\/h3>\n\n\n\n<p><strong>The Law of Cosines relates the lengths of the sides of a triangle with the cosine of one of its angles.<\/strong><\/p>\n\n\n\n<p>The Law of Cosines is also sometimes called the Cosine Rule or Cosine Formula.<\/p>\n\n\n\n<p>If we are given two sides and an included angle (SAS) or three sides (SSS) then we can use the Law of Cosines to solve the triangle i.e. to find all the unknown sides and angles.<\/p>\n\n\n\n<p>We can use the\u00a0Law of Sines\u00a0to solve triangles when we are given two angles and a side (AAS or ASA) or two sides and a non-included angle (SSA).<\/p>\n\n\n\n<p>The Law of Cosines, for any triangle ABC is<\/p>\n\n\n\n<p>a<sup>2<\/sup>&nbsp;= b<sup>2<\/sup>&nbsp;+ c&nbsp;<sup>2<\/sup>&nbsp;\u2013 2bccos A<br>b<sup>2<\/sup>&nbsp;= a<sup>2<\/sup>&nbsp;+ c&nbsp;<sup>2<\/sup>&nbsp;\u2013 2ac cos B<br>c<sup>2<\/sup>&nbsp;= a<sup>2<\/sup>&nbsp;+ b&nbsp;<sup>2<\/sup>&nbsp;\u2013 2ab cos C<\/p>\n\n\n\n<p>The following diagram shows the Law of Cosines. Scroll down the page if you need more examples and solutions on how to use the Law of Cosines and how to proof the Law of Cosines.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/law-of-cosines.png\" alt=\"Law of Cosines\" title=\"Law of Cosines\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"inc-ang\">Law of Cosines: Given two sides and an included-angle<\/h3>\n\n\n\n<p><strong>Example:<\/strong><br>Solve triangle PQR in which p = 6.5 cm, q = 7.4 cm and \u2220R = 58\u00b0.<\/p>\n\n\n\n<p><strong>Solution:<\/strong><br><img loading=\"lazy\" decoding=\"async\" height=\"145\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/law-of-cosines1.jpg\" width=\"177\"><\/p>\n\n\n\n<p>Using the Cosine rule,<\/p>\n\n\n\n<p>r<sup>2<\/sup>&nbsp;= p<sup>2<\/sup>&nbsp;+ q<sup>2<\/sup>\u2013 2pq cos R<\/p>\n\n\n\n<p>r<sup>2<\/sup>&nbsp;= (6.5)<sup>2<\/sup>&nbsp;+ (7.4)<sup>2<\/sup>&nbsp;\u2013 2(6.5)(7.4) cos58\u00b0<br>= 46.03<\/p>\n\n\n\n<p>r = 6.78 cm<\/p>\n\n\n\n<p>Using the Sine rule,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/law-of-cosines2.gif\" alt=\"\"\/><\/figure>\n\n\n\n<p>\u2220Q = 180\u00b0 \u2013 58\u00b0 \u2013 54.39\u00b0<br>= 67.61\u00b0<\/p>\n\n\n\n<p>\u2220P = 54.39\u00b0, \u2220Q = 67.61\u00b0 and r = 6.78 cm<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In these lessons, we will learn: the Law of Cosines how to use the Law of Cosines when given two sides and an included angle how to use the Law of Cosines when given three sides how to proof the Law of Cosines how to solve applications or word problems using the Law of Cosine [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[369],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7631"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=7631"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7631\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=7631"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=7631"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=7631"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}