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Study Guides > Precalculus II

Solutions for Non-Right Triangles: Law of Sines

Solutions to Try Its

1. α=98a=34.6β=39b=22γ=43c=23.8\begin{array}{l}\alpha ={98}^{\circ }a=34.6\\ \beta ={39}^{\circ }b=22\\ \gamma ={43}^{\circ }c=23.8\end{array} 2. Solution 1 α=80a=120β83.2b=121γ16.8c35.2\begin{array}{ll}\alpha =80^\circ \hfill & a=120\hfill \\ \beta \approx 83.2^\circ \hfill & b=121\hfill \\ \gamma \approx 16.8^\circ \hfill & c\approx 35.2\hfill \end{array} Solution 2 α=80a=120β96.8b=121γ3.2c6.8\begin{array}{l}{\alpha }^{\prime }=80^\circ {a}^{\prime }=120\hfill \\ {\beta }^{\prime }\approx 96.8^\circ {b}^{\prime }=121\hfill \\ {\gamma }^{\prime }\approx 3.2^\circ {c}^{\prime }\approx 6.8\hfill \end{array} 3. β5.7,γ94.3,c101.3\beta \approx 5.7^\circ ,\gamma \approx 94.3^\circ ,c\approx 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,a12.0,b19.9 \beta =72^\circ ,a\approx 12.0,b\approx 19.9 9. γ=20,b4.5,c1.6 \gamma =20^\circ ,b\approx 4.5,c\approx 1.6 11. b3.78b\approx 3.78 13. c13.70c\approx 13.70 15. one triangle, α50.3,β16.7,a26.7\alpha \approx 50.3^\circ ,\beta \approx 16.7^\circ ,a\approx 26.7 17. two triangles, γ54.3,β90.7,b20.9 \gamma \approx 54.3^\circ ,\beta \approx 90.7^\circ ,b\approx 20.9 or γ125.7,β19.3,b6.9 {\gamma }^{\prime }\approx 125.7^\circ ,{\beta }^{\prime }\approx 19.3^\circ ,{b}^{\prime }\approx 6.9 19. two triangles, β75.7,γ61.3,b9.9 \beta \approx 75.7^\circ , \gamma \approx 61.3^\circ ,b\approx 9.9 or β18.3,γ118.7,b3.2 {\beta }^{\prime }\approx 18.3^\circ ,{\gamma }^{\prime }\approx 118.7^\circ ,{b}^{\prime }\approx 3.2 21. two triangles, α143.2,β26.8,a17.3\alpha \approx 143.2^\circ ,\beta \approx 26.8^\circ ,a\approx 17.3 or α16.8,β153.2,a8.3{\alpha }^{\prime }\approx 16.8^\circ ,{\beta }^{\prime }\approx 153.2^\circ ,{a}^{\prime }\approx 8.3 23. no triangle possible 25. A47.8A\approx 47.8^\circ or A132.2{A}^{\prime }\approx 132.2^\circ 27. 8.68.6 29. 370.9370.9 31. 12.312.3 33. 12.212.2 35. 16.016.0 37. 29.729.7^\circ 39. x=76.9or x=103.1x=76.9^\circ \text{or }x=103.1^\circ 41. 110.6110.6^\circ 43. A39.4, C47.6, BC20.7A\approx 39.4,\text{ }C\approx 47.6,\text{ }BC\approx 20.7 45. 57.157.1 47. 42.042.0 49. 430.2430.2 51. 10.110.1 53. AD 13.8AD\approx \text{ }13.8 55. AB2.8AB\approx 2.8 57. L49.7, N56.3, LN5.8L\approx 49.7,\text{ }N\approx 56.3,\text{ }LN\approx 5.8 59. 51.4 feet 61. The distance from the satellite to station AA 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

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