Question

Solve the triangle with the law of sines

Answer 1

see below

Explanation:

We can use the law of sines

sin 80 sin B

--------------- = -------------

31 14

Using cross products

14 sin 80 = 31 sin B

14/31 sin 80 = sin B

.984807753 = sin B

Taking the inverse sin of each side

sin ^ -1 ( .444751888) = B

26.41 = B

The sum of the angles of a triangle is 180

A+B+C = 180

80 + 26.41 + C =180

106.41 + C = 180

C = 73.59

We can use the law of sines to find c

sin 80 sin 73.59

--------------- = -------------

31 c

c sin 80 = 31 sin 73.59

c = 31 sin 73.59 / sin 80

c = 30.20

AB = 30.20