Question

solve the right triangle abc, with c = 90°. a = 49.7°, c = 18.8 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°. In a right - triangle with C = 90° and A = 49.7°, we use the formula B=180° - A - C.
B = 180°-90° - 49.7°=40.3°

Step2: Find side a

We use the sine function sin(A)=\frac{a}{c}. Given c = 18.8 ft and A = 49.7°, we can solve for a.
a = c×sin(A)=18.8×sin(49.7°)
a = 18.8×0.762≈14.3 ft

Step3: Find side b

We use the cosine function cos(A)=\frac{b}{c}. Given c = 18.8 ft and A = 49.7°, we can solve for b.
b = c×cos(A)=18.8×cos(49.7°)
b = 18.8×0.648≈12.2 ft

Answer:

B = 40.3°
a = 14.3 ft
b = 12.2 ft