Question

Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. B = 15° C = 113° b = 49

A. A = 50°, a = 176.3, c = 151.2
B. A = 52°, a = 149.2, c = 174.3
C. A = 52°, a = 151.2, c = 176.3
D. A = 50°, a = 174.3, c = 149.2

Answer 1

So,Given that you have A = 23 degrees , B = 21 degrees ,
and side a = 42.8, we find the angle C and the remaining sides of the triangle to be as follows:


Calculating for C = 180 degrees - ( A + B ).
C = 180 - 44 = 136

a / sin A = b / sin B = c / sin C

b = a sin B/ sin A = 42.8 sin 21 / sin 23 = 39.3
c = a sin C/ sin A = 42.8 sin 136/ sin 23 = 76.1

42.8/sin 23 = 109.5
39.3/sin 21 = 109.7
76.1/sin 136 = 109.6


The correct answer is ( c ). C = 136, b = 39.3 , and c = 76.1.