{"id":14143,"date":"2018-06-15T19:21:56","date_gmt":"2018-06-15T19:21:56","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ccbcmd-math\/chapter\/solutions-32\/"},"modified":"2021-11-22T22:09:20","modified_gmt":"2021-11-22T22:09:20","slug":"solutions-law-of-cosines","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/solutions-law-of-cosines\/","title":{"raw":"Solutions: Law of Cosines","rendered":"Solutions: Law of Cosines"},"content":{"raw":"

Solutions to Try Its<\/h2>\r\n1.\u00a0[latex]a\\approx 14.9,\\beta \\approx 23.8^\\circ ,\\gamma \\approx 126.2^\\circ [\/latex].\r\n\r\n2.\u00a0[latex]\\alpha \\approx 27.7^\\circ ,\\beta \\approx 40.5^\\circ ,\\gamma \\approx 111.8^\\circ [\/latex]\r\n\r\n3.\u00a0Area = 552 square feet\r\n\r\n4.\u00a0about 8.15 square feet\r\n

Solutions to Odd-Numbered Exercises<\/h2>\r\n1.\u00a0two sides and the angle opposite the missing side\r\n\r\n3.\u00a0[latex]s[\/latex] is the semi-perimeter, which is half the perimeter of the triangle.\r\n\r\n5.\u00a0The Law of Cosines must be used for any oblique (non-right) triangle.\r\n\r\n7.\u00a011.3\r\n\r\n9.\u00a034.7\r\n\r\n11.\u00a026.7\r\n\r\n13.\u00a0257.4\r\n\r\n15.\u00a0not possible\r\n\r\n17.\u00a095.5\u00b0\r\n\r\n19.\u00a026.9\u00b0\r\n\r\n21.\u00a0[latex]B\\approx 45.9^\\circ ,C\\approx 99.1^\\circ ,a\\approx 6.4[\/latex]\r\n\r\n23.\u00a0[latex]A\\approx 20.6^\\circ ,B\\approx 38.4^\\circ ,c\\approx 51.1[\/latex]\r\n\r\n25.\u00a0[latex]A\\approx 37.8^\\circ ,B\\approx 43.8,C\\approx 98.4^\\circ [\/latex]\r\n\r\n27.\u00a0177.56 in2\r\n\r\n29.\u00a00.04 m2\r\n\r\n31.\u00a00.91 yd2\r\n\r\n33.\u00a03.0\r\n\r\n35.\u00a029.1\r\n\r\n37.\u00a00.5\r\n\r\n39.\u00a070.7\u00b0\r\n\r\n41.\u00a077.4\u00b0\r\n\r\n43.\u00a025.0\r\n\r\n45.\u00a09.3\r\n\r\n47.\u00a043.52\r\n\r\n49.\u00a01.41\r\n\r\n51.\u00a00.14\r\n\r\n53.\u00a018.3\r\n\r\n55.\u00a048.98\r\n\r\n57.\r\n\"A\r\n\r\n59.\u00a07.62\r\n\r\n61.\u00a085.1\r\n\r\n63.\u00a024.0 km\r\n\r\n65.\u00a099.9 ft\r\n\r\n67.\u00a037.3 miles\r\n\r\n69.\u00a02371 miles\r\n\r\n71.\r\n\"Angle\r\n\r\n73.\u00a0599.8 miles\r\n\r\n75.\u00a065.4 cm2\r\n\r\n77.\u00a0468 ft2","rendered":"

Solutions to Try Its<\/h2>\n

1.\u00a0[latex]a\\approx 14.9,\\beta \\approx 23.8^\\circ ,\\gamma \\approx 126.2^\\circ[\/latex].<\/p>\n

2.\u00a0[latex]\\alpha \\approx 27.7^\\circ ,\\beta \\approx 40.5^\\circ ,\\gamma \\approx 111.8^\\circ[\/latex]<\/p>\n

3.\u00a0Area = 552 square feet<\/p>\n

4.\u00a0about 8.15 square feet<\/p>\n

Solutions to Odd-Numbered Exercises<\/h2>\n

1.\u00a0two sides and the angle opposite the missing side<\/p>\n

3.\u00a0[latex]s[\/latex] is the semi-perimeter, which is half the perimeter of the triangle.<\/p>\n

5.\u00a0The Law of Cosines must be used for any oblique (non-right) triangle.<\/p>\n

7.\u00a011.3<\/p>\n

9.\u00a034.7<\/p>\n

11.\u00a026.7<\/p>\n

13.\u00a0257.4<\/p>\n

15.\u00a0not possible<\/p>\n

17.\u00a095.5\u00b0<\/p>\n

19.\u00a026.9\u00b0<\/p>\n

21.\u00a0[latex]B\\approx 45.9^\\circ ,C\\approx 99.1^\\circ ,a\\approx 6.4[\/latex]<\/p>\n

23.\u00a0[latex]A\\approx 20.6^\\circ ,B\\approx 38.4^\\circ ,c\\approx 51.1[\/latex]<\/p>\n

25.\u00a0[latex]A\\approx 37.8^\\circ ,B\\approx 43.8,C\\approx 98.4^\\circ[\/latex]<\/p>\n

27.\u00a0177.56 in2<\/p>\n

29.\u00a00.04 m2<\/p>\n

31.\u00a00.91 yd2<\/p>\n

33.\u00a03.0<\/p>\n

35.\u00a029.1<\/p>\n

37.\u00a00.5<\/p>\n

39.\u00a070.7\u00b0<\/p>\n

41.\u00a077.4\u00b0<\/p>\n

43.\u00a025.0<\/p>\n

45.\u00a09.3<\/p>\n

47.\u00a043.52<\/p>\n

49.\u00a01.41<\/p>\n

51.\u00a00.14<\/p>\n

53.\u00a018.3<\/p>\n

55.\u00a048.98<\/p>\n

57.
\n\"A<\/p>\n

59.\u00a07.62<\/p>\n

61.\u00a085.1<\/p>\n

63.\u00a024.0 km<\/p>\n

65.\u00a099.9 ft<\/p>\n

67.\u00a037.3 miles<\/p>\n

69.\u00a02371 miles<\/p>\n

71.
\n\"Angle<\/p>\n

73.\u00a0599.8 miles<\/p>\n

75.\u00a065.4 cm2<\/p>\n

77.\u00a0468 ft2<\/p>\n\n\t\t\t

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Candela Citations<\/h3>\n\t\t\t\t\t
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