Question

solve the right triangle shown in the figure. a = 59.8°, c = 57 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, the sum of the two non - right angles is 90°. So $B = 90^{\circ}-A$.
$B=90^{\circ}- 59.8^{\circ}=30.2^{\circ}$

Step2: Find side a

Use the sine function $\sin A=\frac{a}{c}$. Then $a = c\times\sin A$.
$a = 57\times\sin(59.8^{\circ})$
$a = 57\times0.8647$ (approx., $\sin(59.8^{\circ})\approx0.8647$)
$a\approx49.29$

Step3: Find side b

Use the cosine function $\cos A=\frac{b}{c}$. Then $b = c\times\cos A$.
$b = 57\times\cos(59.8^{\circ})$
$b = 57\times0.5028$ (approx., $\cos(59.8^{\circ})\approx0.5028$)
$b\approx28.66$

Answer:

$a\approx49.29$