Solve the triangle a 8345 in c 6372 in B 7146 degree What

Solve the triangle. a = 8.345 in c = 6.372 in B = 71.46 degree What is the length of side b? in (Round to the nearest thousandth as needed.) What is the measure of angle A? degree (Round to the nearest hundredth as needed.) What is the measure of angle C? degree (Round to the nearest hundredth as needed.)

Solution

a = 8.345 in

c = 6.372 in

B = 71.46 degrees

applying law of cosines

b^2 = a^2 + c^2 - 2ac cos B

b^2 = 8.345^2 + 6.372^2 - 2(8.345)(6.372) cos B

b = 8.742 in

applying law of sines to find A

a / sin A = b / sin B

8.345 / sin A = 8.742 / sin 71.46

A = 64.83 degrees

again applying law of sines

c / sin C = 8.742 / sin 71.46

6.372 / sin C = 8.742 / sin 71.46

C = 43.71 degrees