Solutions for Right Triangle Trigonometry

Solutions to Try Its

1. [latex]\frac{7}{25}[/latex]

2. [latex]\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}[/latex]

3. [latex]\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[/latex],

[latex]\sec \left(\frac{\pi }{4}\right)=\sqrt{2},csc\left(\frac{\pi }{4}\right)=\sqrt{2},\cot \left(\frac{\pi }{4}\right)=1[/latex]

4. 2

5. [latex]\text{adjacent}=10[/latex]; [latex]\text{opposite}=10\sqrt{3}[/latex] ; missing angle is [latex]\frac{\pi }{6}[/latex]

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. [latex]\frac{\pi }{6}[/latex]

9. [latex]\frac{\pi }{4}[/latex]

11. [latex]b=\frac{20\sqrt{3}}{3},c=\frac{40\sqrt{3}}{3}[/latex]

13. [latex]a=10,000,c=10,000.5[/latex]

15. [latex]b=\frac{5\sqrt{3}}{3},c=\frac{10\sqrt{3}}{3}[/latex]

17. [latex]\frac{5\sqrt{29}}{29}[/latex]

19. [latex]\frac{5}{2}[/latex]

21. [latex]\frac{\sqrt{29}}{2}[/latex]

23. [latex]\frac{5\sqrt{41}}{41}[/latex]

25. [latex]\frac{5}{4}[/latex]

27. [latex]\frac{\sqrt{41}}{4}[/latex]

29. [latex]c=14, b=7\sqrt{3}[/latex]

31. [latex]a=15, b=15[/latex]

33. [latex]b=9.9970, c=12.2041[/latex]

35. [latex]a=2.0838, b=11.8177[/latex]

37. [latex]a=55.9808,c=57.9555[/latex]

39. [latex]a=46.6790,b=17.9184[/latex]

41. [latex]a=16.4662,c=16.8341[/latex]

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