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Study Guides > Precalculus II

Solutions for Right Triangle Trigonometry

Solutions to Try Its

1. 725\frac{7}{25} 2. sint=3365,cost=5665,tant=3356,sect=6556,csct=6533,cott=5633\begin{array}{l}sin t=\frac{33}{65},\cos t=\frac{56}{65},tan t=\frac{33}{56},\hfill \\ \sec t=\frac{65}{56},\csc t=\frac{65}{33},\cot t=\frac{56}{33}\hfill \end{array} 3. sin(π4)=22,cos(π4)=22,tan(π4)=1\sin \left(\frac{\pi }{4}\right)=\frac{\sqrt{2}}{2},\cos \left(\frac{\pi }{4}\right)=\frac{\sqrt{2}}{2},\tan \left(\frac{\pi }{4}\right)=1, sec(π4)=2,csc(π4)=2,cot(π4)=1\sec \left(\frac{\pi }{4}\right)=\sqrt{2},csc\left(\frac{\pi }{4}\right)=\sqrt{2},\cot \left(\frac{\pi }{4}\right)=1 4. 2 5. adjacent=10\text{adjacent}=10; opposite=103\text{opposite}=10\sqrt{3} ; missing angle is π6\frac{\pi }{6} 6. About 52 ft

Solutions to Odd-Numbered Exercises

1. A right triangle with side opposite, adjacent, and hypotenuse labeled. 3. The tangent of an angle is the ratio of the opposite side to the adjacent side. 5. For example, the sine of an angle is equal to the cosine of its complement; the cosine of an angle is equal to the sine of its complement. 7. π6\frac{\pi }{6} 9. π4\frac{\pi }{4} 11. b=2033,c=4033b=\frac{20\sqrt{3}}{3},c=\frac{40\sqrt{3}}{3} 13. a=10,000,c=10,000.5a=10,000,c=10,000.5 15. b=533,c=1033b=\frac{5\sqrt{3}}{3},c=\frac{10\sqrt{3}}{3} 17. 52929\frac{5\sqrt{29}}{29} 19. 52\frac{5}{2} 21. 292\frac{\sqrt{29}}{2} 23. 54141\frac{5\sqrt{41}}{41} 25. 54\frac{5}{4} 27. 414\frac{\sqrt{41}}{4} 29. c=14,b=73c=14, b=7\sqrt{3} 31. a=15,b=15a=15, b=15 33. b=9.9970,c=12.2041b=9.9970, c=12.2041 35. a=2.0838,b=11.8177a=2.0838, b=11.8177 37. a=55.9808,c=57.9555a=55.9808,c=57.9555 39. a=46.6790,b=17.9184a=46.6790,b=17.9184 41. a=16.4662,c=16.8341a=16.4662,c=16.8341 43. 188.3159 45. 200.6737 47. 498.3471 ft 49. 1060.09 ft 51. 27.372 ft 53. 22.6506 ft 55. 368.7633 ft

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  • Precalculus. Provided by: OpenStax Authored by: OpenStax College. Located at: https://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1/Preface. License: CC BY: Attribution.