1. α=98∘a=34.6β=39∘b=22γ=43∘c=23.8
2.
Solution 1α=80∘β≈83.2∘γ≈16.8∘a=120b=121c≈35.2Solution 2α′=80∘a′=120β′≈96.8∘b′=121γ′≈3.2∘c′≈6.8
3. β≈5.7∘,γ≈94.3∘,c≈101.3
4. two
5. about 8.2 square feet
6. 161.9 yd
Solutions to Odd-Numbered Exercises
1. The altitude extends from any vertex to the opposite side or to the line containing the opposite side at a 90° angle.
3. When the known values are the side opposite the missing angle and another side and its opposite angle.
5. A triangle with two given sides and a non-included angle.
7. β=72∘,a≈12.0,b≈19.9
9. γ=20∘,b≈4.5,c≈1.6
11. b≈3.78
13. c≈13.70
15. one triangle, α≈50.3∘,β≈16.7∘,a≈26.7
17. two triangles, γ≈54.3∘,β≈90.7∘,b≈20.9 or γ′≈125.7∘,β′≈19.3∘,b′≈6.9
19. two triangles, β≈75.7∘,γ≈61.3∘,b≈9.9 or β′≈18.3∘,γ′≈118.7∘,b′≈3.2
21. two triangles, α≈143.2∘,β≈26.8∘,a≈17.3 or α′≈16.8∘,β′≈153.2∘,a′≈8.3
23. no triangle possible
25. A≈47.8∘ or A′≈132.2∘
27. 8.6
29. 370.9
31. 12.3
33. 12.2
35. 16.0
37. 29.7∘
39. x=76.9∘or x=103.1∘
41. 110.6∘
43. A≈39.4,C≈47.6,BC≈20.7
45. 57.1
47. 42.0
49. 430.2
51. 10.1
53. AD≈13.8
55. AB≈2.8
57. L≈49.7,N≈56.3,LN≈5.8
59. 51.4 feet
61. The distance from the satellite to station A is approximately 1716 miles. The satellite is approximately 1706 miles above the ground.
63. 2.6 ft
65. 5.6 km
67. 371 ft
69. 5936 ft
71. 24.1 ft
73. 19,056 ft2
75. 445,624 square miles
77. 8.65 ft2