Solutions for Non-Right Triangles: Law of Cosines

Solutions to Try Its

1. [latex]a\approx 14.9,\beta \approx 23.8^\circ ,\gamma \approx 126.2^\circ [/latex].

2. [latex]\alpha \approx 27.7^\circ ,\beta \approx 40.5^\circ ,\gamma \approx 111.8^\circ [/latex]

3. Area = 552 square feet

4. about 8.15 square feet

Solutions to Odd-Numbered Exercises

1. two sides and the angle opposite the missing side

3. [latex]s[/latex] is the semi-perimeter, which is half the perimeter of the triangle.

5. The Law of Cosines must be used for any oblique (non-right) triangle.

7. 11.3

9. 34.7

11. 26.7

13. 257.4

15. not possible

17. 95.5°

19. 26.9°

21. [latex]B\approx 45.9^\circ ,C\approx 99.1^\circ ,a\approx 6.4[/latex]

23. [latex]A\approx 20.6^\circ ,B\approx 38.4^\circ ,c\approx 51.1[/latex]

25. [latex]A\approx 37.8^\circ ,B\approx 43.8,C\approx 98.4^\circ [/latex]

27. 177.56 in2

29. 0.04 m2

31. 0.91 yd2

33. 3.0

35. 29.1

37. 0.5

39. 70.7°

41. 77.4°

43. 25.0

45. 9.3

47. 43.52

49. 1.41

51. 0.14

53. 18.3

55. 48.98

57.
A triangle. One angle is 52 degrees with opposite side = x. The other two sides are 5 and 6.

59. 7.62

61. 85.1

63. 24.0 km

65. 99.9 ft

67. 37.3 miles

69. 2371 miles

71.
Angle BO is 9.1 degrees, angle PH is 150.2 degrees, and angle DC is 20.7 degrees.

73. 599.8 miles

75. 65.4 cm2

77. 468 ft2