Find the unknown sides of the right triangle (see illustration). Round your answer to the appropriate number of significant digits. $$c = 185.2 \mathrm {~cm} , \angle B = 61.47 ^ { \circ }$$
A) a = 210.8 m, b = 100.7 m
B) a = 387.8 m, b = 210.8 m
C) a = 88.46 m, b = 162.7 m
D) a = 181.6 m, b = 36.34 m
E) a = 100.7 m, b = 340.7 m

Question

Find the unknown sides of the right triangle (see illustration). Round your answer to the appropriate number of significant digits. $$c = 185.2 \mathrm {~cm} , \angle B = 61.47 ^ { \circ }$$ 
A) a = 210.8 m, b = 100.7 m 
B) a = 387.8 m, b = 210.8 m 
C) a = 88.46 m, b = 162.7 m 
D) a = 181.6 m, b = 36.34 m 
E) a = 100.7 m, b = 340.7 m

Quizplus · Accepted Answer

Using trigonometric ratios, we have:
$\sin B = \frac{a}{c}$ and $\cos B = \frac{b}{c}$
Substituting the given values, we get:
$\sin 61.47 ^{\circ} = \frac{a}{185.2}$ and $\cos 61.47 ^{\circ} = \frac{b}{185.2}$
Solving for $a$ and $b$, we get:
$a = 88.46$ and $b = 162.7$
Thus, the correct answer is (C).

Find the Unknown Sides of the Right Triangle (See Illustration) c=185.2 cm,∠B=61.47∘c = 185.2 \mathrm {~cm} , \angle B = 61.47 ^ { \circ }c=185.2 cm,∠B=61.47∘

Find the Unknown Sides of the Right Triangle (See Illustration) $c = 185.2 \mathrm {~cm} , \angle B = 61.47 ^ { \circ }$