Question

solve the right triangle shown in the figure. a = 58°, c = 59
a. what are the lengths of the sides?
a ≈ (round to the nearest hundredth as needed.)
b ≈ (round to the nearest hundredth as needed.)
b. what are the angles?
b = ° (round to the nearest tenth as needed.)
c = °

Explanation:

Step1: Find angle B

In a right - triangle, the sum of the interior angles is 180°. Since C = 90° and A = 58°, then B=180° - 90° - 58° = 32°.

Step2: Find side a

We know that $\sin A=\frac{a}{c}$. Given A = 58° and c = 59, then $a = c\times\sin A=59\times\sin(58^{\circ})\approx59\times0.8480\approx49.93$.

Step3: Find side b

We know that $\cos A=\frac{b}{c}$. Given A = 58° and c = 59, then $b = c\times\cos A=59\times\cos(58^{\circ})\approx59\times0.5299\approx31.26$.

Answer:

a. $a\approx49.93$, $b\approx31.26$
b. $B = 32.0^{\circ}$, $C = 90^{\circ}$