SOLUTION: Suppose there is a triangle with sides a, b, and c and angles A, B, and C. Using the known given information below and the law of sines, what is the measure of side c? Round you

Algebra ->  Triangles -> SOLUTION: Suppose there is a triangle with sides a, b, and c and angles A, B, and C. Using the known given information below and the law of sines, what is the measure of side c? Round you      Log On


   

Question 1084116: Suppose there is a triangle with sides a, b, and c and angles A, B, and
C. Using the known given information below and the law of sines, what is the measure of side c? Round your answers to the nearest whole number, if necessary.
b = 23 cm
a = 14 cm
B = 105°
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the law of sines,
sin%28B%29%2Fb=sin%28A%29%2Fa
sin%28105%29%2F23=sin%28A%29%2F14
sin%28A%29=%2814%2F23%29%280.9659%29
sin%28A%29=0.5880
A=36.012
So then,
A%2BB%2BC=180
36.012%2B105%2BC%2B180
C=38.988
Use the law of sines again,
sin%28C%29%2Fc=sin%28B%29%2Fb
sin%2838.988%29%2Fc=sin%28105%29%2F23
c=23%2A%28sin%2838.988%29%2Fsin%28105%29%29
c=14.98cm