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-display]\sec \left(\frac{\pi }{4}\right)=\sqrt{2},csc\left(\frac{\pi }{4}\right)=\sqrt{2},\cot \left(\frac{\pi }{4}\right)=1[/latex-display] 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 ftSolutions to Odd-Numbered Exercises
1.
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 ftLicenses & Attributions
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- Precalculus. Provided by: OpenStax Authored by: OpenStax College. Located at: https://cnx.org/contents/[email protected]:1/Preface. License: CC BY: Attribution.
