Find the unknown sides of the right triangle (see illustration). Round your answer to the appropriate number of significant digits. $$b = 29,400 \mathrm {~km} , \angle A = 12.4 ^ { \circ }$$
A) a = 6,310 km, c = 134,000 km
B) a = 20,400 km, c = 35,800 km
C) a = 6,460 km, c = 30,100 km
D) a = 137,000 km, c = 6,310 km
E) a = 134,000 km, c = 28,700 km

Question

Find the unknown sides of the right triangle (see illustration). Round your answer to the appropriate number of significant digits. $$b = 29,400 \mathrm {~km} , \angle A = 12.4 ^ { \circ }$$ 
A) a = 6,310 km, c = 134,000 km 
B) a = 20,400 km, c = 35,800 km 
C) a = 6,460 km, c = 30,100 km 
D) a = 137,000 km, c = 6,310 km 
E) a = 134,000 km, c = 28,700 km

Quizplus · Accepted Answer

Using trigonometry, we can solve for the missing sides of the right triangle. We know that $	an \angle A = \frac{a}{b}$, so $a = b 	an \angle A = (29,400 \mathrm{~km}) 	an(12.4^\circ) = 6,460\mathrm{~km}$.

We also know that $\sin \angle A = \frac{c}{b}$, so $c = b \sin \angle A = (29,400 \mathrm{~km}) \sin(12.4^\circ) = 30,100\mathrm{~km}$.

Therefore, the missing sides are $a = 6,460\mathrm{~km}$ and $c = 30,100\mathrm{~km}$, and the answer is choice C.

Find the Unknown Sides of the Right Triangle (See Illustration) b=29,400 km,∠A=12.4∘b = 29,400 \mathrm {~km} , \angle A = 12.4 ^ { \circ }b=29,400 km,∠A=12.4∘

Find the Unknown Sides of the Right Triangle (See Illustration) $b = 29,400 \mathrm {~km} , \angle A = 12.4 ^ { \circ }$