Question

find the value of \x\. round sides to 4 places past the decimal and angles to the nearest whole degree. 1. 16 10 x° 2. x 17° 9.7 3. x 63° 50 4. x° 7 13 5. 15 25° x 6. x 32° 24 7. 12 15 x° 8. 5.8 18° x 9. x 30° 20 10. x 17 65°

Explanation:

Step1: 삼각함수 정의 사용

삼각함수 $\tan$, $\sin$, $\cos$ 정의를 이용해 각 문제에서 $x$ 값을 구합니다. $\tan\theta=\frac{\text{반대변}}{\text{인접변}}$, $\sin\theta=\frac{\text{반대변}}{\text{빗변}}$, $\cos\theta=\frac{\text{인접변}}{\text{빗변}}$입니다.

1. $\tan x=\frac{10}{16}$, $x = \arctan(\frac{10}{16})\approx32.0054^{\circ}$
2. $\cos17^{\circ}=\frac{x}{9.7}$, $x = 9.7\times\cos17^{\circ}\approx9.2713$
3. $\sin63^{\circ}=\frac{x}{50}$, $x = 50\times\sin63^{\circ}\approx44.5892$
4. $\sin x=\frac{7}{13}$, $x=\arcsin(\frac{7}{13})\approx32^{\circ}$
5. $\tan25^{\circ}=\frac{x}{15}$, $x = 15\times\tan25^{\circ}\approx6.9907$
6. $\sin32^{\circ}=\frac{x}{24}$, $x = 24\times\sin32^{\circ}\approx12.7167$
7. $\tan x=\frac{15}{12}$, $x=\arctan(\frac{15}{12})\approx51^{\circ}$
8. $\cos18^{\circ}=\frac{5.8}{x}$, $x=\frac{5.8}{\cos18^{\circ}}\approx6.1081$
9. $\tan30^{\circ}=\frac{20}{x}$, $x=\frac{20}{\tan30^{\circ}}\approx34.6410$
10. $\sin65^{\circ}=\frac{x}{17}$, $x = 17\times\sin65^{\circ}\approx15.4035$

Answer:

1. $x\approx32.0054^{\circ}$
2. $x\approx9.2713$
3. $x\approx44.5892$
4. $x\approx32^{\circ}$
5. $x\approx6.9907$
6. $x\approx12.7167$
7. $x\approx51^{\circ}$
8. $x\approx6.1081$
9. $x\approx34.6410$
10. $x\approx15.4035$