Question

find the measure of ∠a and ∠b. round answers to the nearest whole degree.
31.
32.
find the length of the hypotenuse. round answers to 4 places past the decimal.
33.
34.
set up an equation and then solve for \x\. round answers to 4 places past the decimal.
35.
36.
find the measure of ∠a and ∠b. round answers to 4 places past the decimal.
37.
38.

1. find the width of rectangle of abcd.
2. find the length of the altitude the triangle below.

Explanation:

Step1: 문제 31번 - 각도 계산

삼각형에서 $\sin A=\frac{BC}{AB}$, $\cos A = \frac{AC}{AB}$을 이용합니다. $AB = 25$, $BC=20$, $AC=\sqrt{25^{2}-20^{2}} = 15$. $\sin A=\frac{20}{25}=0.8$, $A=\sin^{- 1}(0.8)\approx53^{\circ}$, $B = 90^{\circ}-A\approx37^{\circ}$.

Step2: 문제 32번 - 각도 계산

$AB=\sqrt{14^{2}+30^{2}}=\sqrt{196 + 900}=\sqrt{1096}\approx33.1059$. $\sin A=\frac{30}{\sqrt{1096}}\approx0.9062$, $A=\sin^{-1}(0.9062)\approx64^{\circ}$, $B=90^{\circ}-A\approx26^{\circ}$.

Step3: 문제 33번 - 빗변 길이 계산

$\sin47^{\circ}=\frac{BC}{AB}$, $BC = 18$, $AB=\frac{18}{\sin47^{\circ}}\approx\frac{18}{0.7314}\approx24.6104$.

Step4: 문제 34번 - 빗변 길이 계산

$\cos34^{\circ}=\frac{KL}{JL}$, $KL = 9$, $JL=\frac{9}{\cos34^{\circ}}\approx\frac{9}{0.8290}\approx10.8565$.

Step5: 문제 35번 - x 계산

$\tan27^{\circ}=\frac{x}{15}$, $x = 15\times\tan27^{\circ}\approx15\times0.5095\approx7.6428$.

Step6: 문제 36번 - x 계산

$\cos55^{\circ}=\frac{12}{x}$, $x=\frac{12}{\cos55^{\circ}}\approx\frac{12}{0.5736}\approx20.9205$.

Step7: 문제 37번 - 각도 계산

$\tan A=\frac{18}{15}=1.2$, $A=\tan^{-1}(1.2)\approx50.1944^{\circ}$, $B = 90^{\circ}-A\approx39.8056^{\circ}$.

Step8: 문제 38번 - 각도 계산

$\tan A=\frac{6.2}{14}\approx0.4429$, $A=\tan^{-1}(0.4429)\approx23.9625^{\circ}$, $B=90^{\circ}-A\approx66.0375^{\circ}$.

Step9: 문제 39번 - 직사각형 너비 계산

$\tan41^{\circ}=\frac{w}{8}$, $w = 8\times\tan41^{\circ}\approx8\times0.8693\approx6.9546$.

Step10: 문제 40번 - 높이 계산

$\tan54^{\circ}=\frac{h}{3}$ (밑변의 절반은 3), $h = 3\times\tan54^{\circ}\approx3\times1.3764\approx4.1291$.

Answer:

1. $\angle A\approx53^{\circ}$, $\angle B\approx37^{\circ}$
2. $\angle A\approx64^{\circ}$, $\angle B\approx26^{\circ}$
3. $AB\approx24.6104$
4. $JL\approx10.8565$
5. $x\approx7.6428$
6. $x\approx20.9205$
7. $\angle A\approx50.1944^{\circ}$, $\angle B\approx39.8056^{\circ}$
8. $\angle A\approx23.9625^{\circ}$, $\angle B\approx66.0375^{\circ}$
9. $w\approx6.9546$
10. $h\approx4.1291$