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:

문제 31

Step1: $\angle A$ 구하기

$\sin A=\frac{BC}{AB}=\frac{20}{25} = 0.8$
$A=\sin^{- 1}(0.8)\approx53.1301^{\circ}\approx53^{\circ}$

Step2: $\angle B$ 구하기

$\angle A+\angle B = 90^{\circ}$
$\angle B=90^{\circ}-\angle A=90^{\circ}-53^{\circ}=37^{\circ}$

문제 32

Step1: $\sin A=\frac{BC}{AB}$

$AB=\frac{BC}{\sin A}$, $\sin A=\frac{14}{30}\approx0.4667$
$A=\sin^{-1}(0.4667)\approx27.8158^{\circ}\approx28^{\circ}$

Step2: $\angle B$ 구하기

$\angle A+\angle B = 90^{\circ}$
$\angle B=90^{\circ}-\angle A=90^{\circ}-28^{\circ}=62^{\circ}$

문제 33

Step1: $\sin A=\frac{BC}{AB}$

$AB=\frac{BC}{\sin A}$, $A = 47^{\circ}$, $BC = 18$
$AB=\frac{18}{\sin47^{\circ}}\approx\frac{18}{0.7314}\approx24.6104$

문제 34

Step1: $\cos L=\frac{KL}{JL}$

$JL=\frac{KL}{\cos L}$, $KL = 9$, $L = 34^{\circ}$
$JL=\frac{9}{\cos34^{\circ}}\approx\frac{9}{0.8290}\approx10.8565$

문제 35

Step1: $\tan63^{\circ}=\frac{x}{15}$

$x = 15\times\tan63^{\circ}\approx15\times1.9626\approx29.4385$

문제 36

Step1: $\tan55^{\circ}=\frac{12}{x}$

$x=\frac{12}{\tan55^{\circ}}\approx\frac{12}{1.4281}\approx8.4027$

문제 37

Step1: $\tan A=\frac{BC}{AC}$

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

Step2: $\angle B$ 구하기

$\angle A+\angle B = 90^{\circ}$
$\angle B=90^{\circ}-\angle A=90^{\circ}-50.1944^{\circ}=39.8056^{\circ}$

문제 38

Step1: $\tan A=\frac{BC}{AC}$

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

Step2: $\angle B$ 구하기

$\angle A+\angle B = 90^{\circ}$
$\angle B=90^{\circ}-\angle A=90^{\circ}-23.9625^{\circ}=66.0375^{\circ}$

문제 39

Step1: $\tan41^{\circ}=\frac{w}{8}$

$w = 8\times\tan41^{\circ}\approx8\times0.8693\approx6.9544$

문제 40

Step1: $\tan54^{\circ}=\frac{h}{3}$

$h = 3\times\tan54^{\circ}\approx3\times1.3764\approx4.1291$

Answer:

1. $\angle A = 53^{\circ}$, $\angle B = 37^{\circ}$
2. $\angle A\approx28^{\circ}$, $\angle B\approx62^{\circ}$
3. $AB\approx24.6104$
4. $JL\approx10.8565$
5. $x\approx29.4385$
6. $x\approx8.4027$
7. $\angle A\approx50.1944^{\circ}$, $\angle B\approx39.8056^{\circ}$
8. $\angle A\approx23.9625^{\circ}$, $\angle B\approx66.0375^{\circ}$
9. $w\approx6.9544$
10. $h\approx4.1291$