Question

solve the right triangle shown in the figure. a = 57.2°, c = 56 a. what are the lengths of the sides? a ≈ (round to the nearest hundredth as needed.)

Explanation:

Step1: Find angle B

In a right - triangle, $A + B+ C=180^{\circ}$, and $C = 90^{\circ}$. So $B=180^{\circ}-90^{\circ}-A$.
$B = 180^{\circ}-90^{\circ}-57.2^{\circ}=32.8^{\circ}$

Step2: Find side a

Use the sine function $\sin A=\frac{a}{c}$. Then $a = c\times\sin A$.
$a = 56\times\sin(57.2^{\circ})$
$a = 56\times0.8416$ (approx., $\sin(57.2^{\circ})\approx0.8416$)
$a\approx47.13$

Step3: Find side b

Use the cosine function $\cos A=\frac{b}{c}$. Then $b = c\times\cos A$.
$b = 56\times\cos(57.2^{\circ})$
$b = 56\times0.5408$ (approx., $\cos(57.2^{\circ})\approx0.5408$)
$b\approx30.28$

Answer:

$a\approx47.13$, $b\approx30.28$