Solve triangle ABC Round the length to three decimal places

Solve triangle ABC. (Round the length to three decimal places and the angles to one decimal place.) Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that A_1 is smaller than A_2.) b = 122, C = 167, B = 46 degree

Solution

b = 122 , c = 167 , angle B = 46

applying law of sines

b / sin B = c / sin C

122 / sin 46 = 167 / sin C

sin C = 167 / 169.599

C = 79.95 degrees

A2 = 180 - ( 79.95 + 46 ) = 54.05 degrees

a / sin A = b/ sin B

a 2 = 122/ sin 46 * sin 54.05

a2 = 137.30