Question

Determine the remaining sides and angles of the triangle ABC.

c=6 mi, B = 38.71°, C = 32.51°
Find the measure of angle A.
A=°
(Type an integer or a decimal.)
Find the length of side a.
а:
mi
(Round to the nearest mile as needed.)
Find the length of side b.
b=mi
(Round to the nearest mile as needed.)

Answer 1

9514 1404 393

Answer:

A = 108.78°

a = 11 mi

b = 7 mi

Explanation:

The sum of angles in a triangle is 180°, so the third angle is ...

A = 180° -38.71° -32.51°

A = 108.78°

__

The remaining sides can be found from the law of sines.

a/sin(A) = c/sin(C)

a = sin(A)·c/sin(C) ≈ 0.946762 × 11.163896

a ≈ 11 mi

b = sin(B)·11.163896 ≈ 0.625379 × 11.163896

b ≈ 7 mi