{"id":1414,"date":"2023-06-05T14:51:30","date_gmt":"2023-06-05T14:51:30","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/chapter\/solutions-for-non-right-triangles-law-of-sines\/"},"modified":"2023-06-05T14:51:30","modified_gmt":"2023-06-05T14:51:30","slug":"solutions-for-non-right-triangles-law-of-sines","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/chapter\/solutions-for-non-right-triangles-law-of-sines\/","title":{"raw":"Solutions 57: Non-Right Triangles: Law of Sines","rendered":"Solutions 57: Non-Right Triangles: Law of Sines"},"content":{"raw":"\n

Solutions to Odd-Numbered Exercises<\/h2>\n1. The altitude extends from any vertex to the opposite side or to the line containing the opposite side at a 90\u00b0 angle.\n\n3. When the known values are the side opposite the missing angle and another side and its opposite angle.\n\n5. A triangle with two given sides and a non-included angle.\n\n7. [latex] \\beta =72^\\circ ,a\\approx 12.0,b\\approx 19.9[\/latex]\n\n9. [latex] \\gamma =20^\\circ ,b\\approx 4.5,c\\approx 1.6[\/latex]\n\n11. [latex]b\\approx 3.78[\/latex]\n\n13. [latex]c\\approx 13.70[\/latex]\n\n15. one triangle, [latex]\\alpha \\approx 50.3^\\circ ,\\beta \\approx 16.7^\\circ ,a\\approx 26.7[\/latex]\n\n17. two triangles, [latex] \\gamma \\approx 54.3^\\circ ,\\beta \\approx 90.7^\\circ ,b\\approx 20.9[\/latex] or [latex] {\\gamma }^{\\prime }\\approx 125.7^\\circ ,{\\beta }^{\\prime }\\approx 19.3^\\circ ,{b}^{\\prime }\\approx 6.9[\/latex]\n\n19. two triangles, [latex] \\beta \\approx 75.7^\\circ , \\gamma \\approx 61.3^\\circ ,b\\approx 9.9[\/latex] or [latex] {\\beta }^{\\prime }\\approx 18.3^\\circ ,{\\gamma }^{\\prime }\\approx 118.7^\\circ ,{b}^{\\prime }\\approx 3.2[\/latex]\n\n21. two triangles, [latex]\\alpha \\approx 143.2^\\circ ,\\beta \\approx 26.8^\\circ ,a\\approx 17.3[\/latex] or [latex]{\\alpha }^{\\prime }\\approx 16.8^\\circ ,{\\beta }^{\\prime }\\approx 153.2^\\circ ,{a}^{\\prime }\\approx 8.3[\/latex]\n\n23. no triangle possible\n\n25. [latex]A\\approx 47.8^\\circ [\/latex] or [latex]{A}^{\\prime }\\approx 132.2^\\circ [\/latex]\n\n27. [latex]8.6[\/latex]\n\n29. [latex]370.9[\/latex]\n\n31. [latex]12.3[\/latex]\n\n33. [latex]12.2 [\/latex]\n\n35. [latex]16.0 [\/latex]\n\n37. [latex]29.7^\\circ [\/latex]\n\n39. [latex]x=76.9^\\circ \\text{or }x=103.1^\\circ [\/latex]\n\n41. [latex]110.6^\\circ [\/latex]\n\n43. [latex]A\\approx 39.4,\\text{ }C\\approx 47.6,\\text{ }BC\\approx 20.7 [\/latex]\n\n45. [latex]57.1[\/latex]\n\n47. [latex]42.0 [\/latex]\n\n49. [latex]430.2 [\/latex]\n\n51. [latex]10.1[\/latex]\n\n53. [latex]AD\\approx \\text{ }13.8[\/latex]\n\n55. [latex]AB\\approx 2.8 [\/latex]\n\n57. [latex]L\\approx 49.7,\\text{ }N\\approx 56.3,\\text{ }LN\\approx 5.8[\/latex]\n\n59. 51.4 feet\n\n61. The distance from the satellite to station [latex]A[\/latex] is approximately 1716 miles. The satellite is approximately 1706 miles above the ground.\n\n63. 2.6 ft\n\n65. 5.6 km\n\n67. 371 ft\n\n69. 5936 ft\n\n71. 24.1 ft\n\n73. 19,056 ft2\n\n75. 445,624 square miles\n\n77. 8.65 ft2\n","rendered":"

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

1. The altitude extends from any vertex to the opposite side or to the line containing the opposite side at a 90\u00b0 angle.<\/p>\n

3. When the known values are the side opposite the missing angle and another side and its opposite angle.<\/p>\n

5. A triangle with two given sides and a non-included angle.<\/p>\n

7. [latex]\\beta =72^\\circ ,a\\approx 12.0,b\\approx 19.9[\/latex]<\/p>\n

9. [latex]\\gamma =20^\\circ ,b\\approx 4.5,c\\approx 1.6[\/latex]<\/p>\n

11. [latex]b\\approx 3.78[\/latex]<\/p>\n

13. [latex]c\\approx 13.70[\/latex]<\/p>\n

15. one triangle, [latex]\\alpha \\approx 50.3^\\circ ,\\beta \\approx 16.7^\\circ ,a\\approx 26.7[\/latex]<\/p>\n

17. two triangles, [latex]\\gamma \\approx 54.3^\\circ ,\\beta \\approx 90.7^\\circ ,b\\approx 20.9[\/latex] or [latex]{\\gamma }^{\\prime }\\approx 125.7^\\circ ,{\\beta }^{\\prime }\\approx 19.3^\\circ ,{b}^{\\prime }\\approx 6.9[\/latex]<\/p>\n

19. two triangles, [latex]\\beta \\approx 75.7^\\circ , \\gamma \\approx 61.3^\\circ ,b\\approx 9.9[\/latex] or [latex]{\\beta }^{\\prime }\\approx 18.3^\\circ ,{\\gamma }^{\\prime }\\approx 118.7^\\circ ,{b}^{\\prime }\\approx 3.2[\/latex]<\/p>\n

21. two triangles, [latex]\\alpha \\approx 143.2^\\circ ,\\beta \\approx 26.8^\\circ ,a\\approx 17.3[\/latex] or [latex]{\\alpha }^{\\prime }\\approx 16.8^\\circ ,{\\beta }^{\\prime }\\approx 153.2^\\circ ,{a}^{\\prime }\\approx 8.3[\/latex]<\/p>\n

23. no triangle possible<\/p>\n

25. [latex]A\\approx 47.8^\\circ[\/latex] or [latex]{A}^{\\prime }\\approx 132.2^\\circ[\/latex]<\/p>\n

27. [latex]8.6[\/latex]<\/p>\n

29. [latex]370.9[\/latex]<\/p>\n

31. [latex]12.3[\/latex]<\/p>\n

33. [latex]12.2[\/latex]<\/p>\n

35. [latex]16.0[\/latex]<\/p>\n

37. [latex]29.7^\\circ[\/latex]<\/p>\n

39. [latex]x=76.9^\\circ \\text{or }x=103.1^\\circ[\/latex]<\/p>\n

41. [latex]110.6^\\circ[\/latex]<\/p>\n

43. [latex]A\\approx 39.4,\\text{ }C\\approx 47.6,\\text{ }BC\\approx 20.7[\/latex]<\/p>\n

45. [latex]57.1[\/latex]<\/p>\n

47. [latex]42.0[\/latex]<\/p>\n

49. [latex]430.2[\/latex]<\/p>\n

51. [latex]10.1[\/latex]<\/p>\n

53. [latex]AD\\approx \\text{ }13.8[\/latex]<\/p>\n

55. [latex]AB\\approx 2.8[\/latex]<\/p>\n

57. [latex]L\\approx 49.7,\\text{ }N\\approx 56.3,\\text{ }LN\\approx 5.8[\/latex]<\/p>\n

59. 51.4 feet<\/p>\n

61. The distance from the satellite to station [latex]A[\/latex] is approximately 1716 miles. The satellite is approximately 1706 miles above the ground.<\/p>\n

63. 2.6 ft<\/p>\n

65. 5.6 km<\/p>\n

67. 371 ft<\/p>\n

69. 5936 ft<\/p>\n

71. 24.1 ft<\/p>\n

73. 19,056 ft2<\/p>\n

75. 445,624 square miles<\/p>\n

77. 8.65 ft2<\/p>\n\n\t\t\t

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