{"id":7627,"date":"2022-09-16T06:22:50","date_gmt":"2022-09-16T06:22:50","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=7627"},"modified":"2022-09-16T06:22:50","modified_gmt":"2022-09-16T06:22:50","slug":"law-of-sines-ambiguous-case","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/09\/16\/law-of-sines-ambiguous-case\/","title":{"rendered":"Law of Sines &#8211; Ambiguous Case"},"content":{"rendered":"\n<p>We will now consider the situation when we are&nbsp;<strong>given two sides and one angle<\/strong>&nbsp;of a triangle.<\/p>\n\n\n\n<p><strong>Ambiguous Case<\/strong><br>If you are given two sides and a non-included acute angle and the side facing the given angle is less than the other side, you would obtain two sets of answers. The solution is said to be&nbsp;<strong>ambiguous<\/strong>.<\/p>\n\n\n\n<p><strong>Example:<\/strong><br>Solve triangle PQR in which \u2220 P = 56\u00b0, p = 10 cm and q = 12 cm<\/p>\n\n\n\n<p><strong>Solution:<\/strong><br>Notice that we can construct two different triangles from the given information.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/law-of-sines6.jpg\" alt=\"\"\/><\/figure>\n\n\n\n<p>When \u2220 Q = 95.8\u02da, \u2220 R = 180\u02da \u2013 56\u02da \u2013 95.8\u02da = 28.2\u02da<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.onlinemathlearning.com\/image-files\/law-of-sines7.gif\" alt=\"\"\/><\/figure>\n\n\n\n<p>The two sets of solutions are:<br>\u2220 Q = 84.2\u00b0, \u2220 R = 39.8\u00b0, r = 7.72 cm<br>\u2220 Q = 95.8\u00b0, \u2220 R = 28.2\u00b0, r = 5.70 cm<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We will now consider the situation when we are&nbsp;given two sides and one angle&nbsp;of a triangle. Ambiguous CaseIf you are given two sides and a non-included acute angle and the side facing the given angle is less than the other side, you would obtain two sets of answers. The solution is said to be&nbsp;ambiguous. Example:Solve [&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\/7627"}],"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=7627"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7627\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=7627"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=7627"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=7627"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}