Question

solve the right triangle shown in the figure. a = 53.9°, c = 51 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, $B = 90^{\circ}-A$.
$B=90^{\circ}- 53.9^{\circ}=36.1^{\circ}$

Step2: Find side a

Use the sine function: $\sin A=\frac{a}{c}$. Then $a = c\times\sin A$.
$a = 51\times\sin(53.9^{\circ})$
$a = 51\times0.8077\approx41.19$

Step3: Find side b

Use the cosine function: $\cos A=\frac{b}{c}$. Then $b = c\times\cos A$.
$b = 51\times\cos(53.9^{\circ})$
$b = 51\times0.5894\approx30.06$

Answer:

$a\approx41.19$