Question

solve the right triangle abc, with c = 90°. a = 49.3°, c = 23.4 ft b = ° (simplify your answer. type an integer or a decimal. round to the nearest tenth as needed.) a = ft (simplify your answer. type an integer or a decimal. round to the nearest tenth as needed.) b = ft (simplify your answer. type an integer or a decimal. round to the nearest tenth as needed.)

Explanation:

Step1: Find angle B

The sum of angles in a triangle is 180°. Since C = 90° and A = 49.3°, then B=180° - 90° - 49.3°.
$B = 180 - 90 - 49.3=40.7^{\circ}$

Step2: Find side a

Use the sine - ratio $\sin A=\frac{a}{c}$. Given A = 49.3° and c = 23.4 ft, then $a = c\times\sin A$.
$a=23.4\times\sin(49.3^{\circ})\approx23.4\times0.759\approx17.8$ ft

Step3: Find side b

Use the cosine - ratio $\cos A=\frac{b}{c}$. Given A = 49.3° and c = 23.4 ft, then $b = c\times\cos A$.
$b=23.4\times\cos(49.3^{\circ})\approx23.4\times0.650\approx15.2$ ft

Answer:

$B = 40.7^{\circ}$
$a\approx17.8$ ft
$b\approx15.2$ ft