{"id":7625,"date":"2022-09-16T06:22:05","date_gmt":"2022-09-16T06:22:05","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=7625"},"modified":"2022-09-16T06:22:05","modified_gmt":"2022-09-16T06:22:05","slug":"law-of-sines-given-two-angles-and-one-side","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/09\/16\/law-of-sines-given-two-angles-and-one-side\/","title":{"rendered":"Law of Sines: Given Two Angles And One Side"},"content":{"rendered":"\n<p>We will first consider the situation when we are&nbsp;<strong>given 2 angles and one side&nbsp;<\/strong>of a triangle.<\/p>\n\n\n\n<p><strong>Example:<\/strong><br>Solve triangle PQR in which \u2220P = 63.5\u00b0 and \u2220Q = 51.2\u00b0 and r = 6.3 cm.&nbsp;<img loading=\"lazy\" decoding=\"async\" height=\"138\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/law-of-sines4.jpg\" width=\"175\"><\/p>\n\n\n\n<p><strong>Solution:<\/strong><br>First, calculate the third angle.<\/p>\n\n\n\n<p>\u2220 R = 180\u00b0 \u2013 63.5\u00b0 \u2013 51.2\u00b0 = 65.3\u00b0<\/p>\n\n\n\n<p>Next, calculate the sides.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/law-of-sines5.jpg\" alt=\"\"\/><\/figure>\n\n\n\n<p>\u2220 R = 65.3\u00b0, p = 6.21 cm and q = 5.40 cm<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"2sides\">Law of Sines: Given Two Sides And An Obtuse Angle<\/h3>\n\n\n\n<p>We will now consider the situation when we are&nbsp;<strong>given two sides and an obtuse angle<\/strong>&nbsp;of a triangle.<\/p>\n\n\n\n<p><strong>Example:<\/strong><br>Solve \u2206 PQR in which \u2220 P =116\u00b0, p = 8.3 cm and q = 5.4 cm.<\/p>\n\n\n\n<p><strong>Solution:<\/strong><br><img loading=\"lazy\" decoding=\"async\" height=\"301\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/law-of-sines8.jpg\" width=\"233\"><\/p>\n\n\n\n<p>Q cannot be an obtuse angle because the sum of angles in the triangle will exceed 180\u02da. The only valid value for Q is 35.8\u02da.<\/p>\n\n\n\n<p>\u2220 Q = 35.8\u00b0, \u2220 R = 180\u00b0 \u2013 116\u00b0 \u2013 35.8\u00b0 = 28.2\u00b0<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/law-of-sines9.gif\" alt=\"\"\/><\/figure>\n\n\n\n<p>The solution is \u2220 Q = 35.8\u00b0 , \u2220 R = 28.2\u00b0 and r = 4.36 cm<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We will first consider the situation when we are&nbsp;given 2 angles and one side&nbsp;of a triangle. Example:Solve triangle PQR in which \u2220P = 63.5\u00b0 and \u2220Q = 51.2\u00b0 and r = 6.3 cm.&nbsp; Solution:First, calculate the third angle. \u2220 R = 180\u00b0 \u2013 63.5\u00b0 \u2013 51.2\u00b0 = 65.3\u00b0 Next, calculate the sides. \u2220 R = [&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\/7625"}],"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=7625"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7625\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=7625"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=7625"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=7625"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}