Question

solve the right triangle shown in the figure. a = 58.6°, c = 55

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 = 58.6°, then B=180° - 90° - 58.6° = 31.4°.

Step2: Find side a

We know that $\sin A=\frac{a}{c}$. Given A = 58.6° and c = 55, then $a = c\times\sin A=55\times\sin(58.6^{\circ})\approx55\times0.8536\approx46.95$.

Step3: Find side b

We know that $\cos A=\frac{b}{c}$. Given A = 58.6° and c = 55, then $b = c\times\cos A=55\times\cos(58.6^{\circ})\approx55\times0.5207\approx28.64$.

Answer:

a. $a\approx46.95$, $b\approx28.64$
b. $B = 31.4^{\circ}$, $C = 90^{\circ}$