Find the unknown sides of the right triangle (see illustration). Round your answer to the appropriate number of significant digits. $$c= 49.1 \mathrm {~cm} , \angle A = 36.6 ^ { \circ }$$
A) a = 61.2 cm, b = 66.1 cm
B) a = 29.0 cm, b = 39.6 cm
C) a = 36.5 cm, b = 61.2 cm
D) a = 29.3 cm, b = 39.4 cm
E) a = 82.4 cm, b = 36.5 cm

Question

Find the unknown sides of the right triangle (see illustration). Round your answer to the appropriate number of significant digits. $$c= 49.1 \mathrm {~cm} , \angle A = 36.6 ^ { \circ }$$ 
A) a = 61.2 cm, b = 66.1 cm 
B) a = 29.0 cm, b = 39.6 cm 
C) a = 36.5 cm, b = 61.2 cm 
D) a = 29.3 cm, b = 39.4 cm 
E) a = 82.4 cm, b = 36.5 cm

Quizplus · Accepted Answer

We can use the following trigonometric ratios for this problem:
$$\sin A = \frac{a}{c} \implies a = c \cdot \sin A = 49.1 \mathrm{cm} \cdot \sin 36.6^\circ \approx 29.3 \mathrm{cm}$$
$$\cos A = \frac{b}{c} \implies b = c \cdot \cos A = 49.1 \mathrm{cm} \cdot \cos 36.6^\circ \approx 39.4 \mathrm{cm}$$
Therefore, the answer is D.

Find the Unknown Sides of the Right Triangle (See Illustration) c=49.1 cm,∠A=36.6∘c= 49.1 \mathrm {~cm} , \angle A = 36.6 ^ { \circ }c=49.1 cm,∠A=36.6∘

Find the Unknown Sides of the Right Triangle (See Illustration) $c= 49.1 \mathrm {~cm} , \angle A = 36.6 ^ { \circ }$