Solve the right triangle. Round your answer to the appropriate number of significant digits. $$a = 1,250 \mathrm {~km} , b = 1,620 \mathrm {~km}$$
A) $c = 1,250 \mathrm {~km} , \angle A = 22.0 ^ { \circ } , \angle B = 68.0 ^ { \circ }$
B) $c = 2050 \mathrm {~km} , \angle A = 39.3 ^ { \circ } , \angle B = 50.7 ^ { \circ }$
C) $c = 2050 \mathrm {~km} , \angle A = 37.7 ^ { \circ } , \angle B = 52.3 ^ { \circ }$
D) $c = 2050 \mathrm {~km} , \angle A = 37.7 ^ { \circ } , \angle B = 142.3 ^ { \circ }$
E) $c = 1,250 \mathrm {~km} , \angle A = 52.3 ^ { \circ } , \angle B = 37.7 ^ { \circ }$

Question

Solve the right triangle. Round your answer to the appropriate number of significant digits. $$a = 1,250 \mathrm {~km} , b = 1,620 \mathrm {~km}$$ 
A) $c = 1,250 \mathrm {~km} , \angle A = 22.0 ^ { \circ } , \angle B = 68.0 ^ { \circ }$ 
B) $c = 2050 \mathrm {~km} , \angle A = 39.3 ^ { \circ } , \angle B = 50.7 ^ { \circ }$ 
C) $c = 2050 \mathrm {~km} , \angle A = 37.7 ^ { \circ } , \angle B = 52.3 ^ { \circ }$ 
D) $c = 2050 \mathrm {~km} , \angle A = 37.7 ^ { \circ } , \angle B = 142.3 ^ { \circ }$ 
E) $c = 1,250 \mathrm {~km} , \angle A = 52.3 ^ { \circ } , \angle B = 37.7 ^ { \circ }$

Quizplus · Accepted Answer

Using the Pythagorean theorem, we can solve for $c$: \begin{align*}
c^2 &= a^2 + b^2 \
&= (1250)^2 + (1620)^2 \
&= 3,\!031,\!250.
\end{align*}Taking the square root, the value of $c$ is approximately 1743.1 km.

Now we can use the inverse trigonometric functions to solve for the angles. We have: \begin{align*}
\sin A &= \frac{a}{c} \
&= \frac{1250}{1743.1} \
&= 0.7176
\end{align*}Taking the inverse sine, $\angle A$ is approximately 43.4 degrees. Similarly, we can find $\angle B$: \begin{align*}
\sin B &= \frac{b}{c} \
&= \frac{1620}{1743.1} \
&= 0.9308
\end{align*}Taking the inverse sine, $\angle B$ is approximately 68.3 degrees.

Therefore, the answer is $\boxed{	extbf{(C)}}$.

Solve the Right Triangle a=1,250 km,b=1,620 kma = 1,250 \mathrm {~km} , b = 1,620 \mathrm {~km}a=1,250 km,b=1,620 km

Solve the Right Triangle $a = 1,250 \mathrm {~km} , b = 1,620 \mathrm {~km}$