SOLUTION: In triangle ABC, measure of angle A is 32 degrees, AB equals 8 and BC equals 5 Find the 2 possible values of measure angle C.

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Question 1010678: In triangle ABC, measure of angle A is 32 degrees, AB equals 8 and BC equals 5
Find the 2 possible values of measure angle C.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
In triangle ABC, measure of angle A is 32 degrees, AB equals 8 and BC
equals 5. Find the 2 possible values of measure angle C.


By the law of sines:

BC%2Fsin%28%22BAC%22%29%22%22=%22%22AB%2Fsin%28%22ACB%22%29

Cross-multiply

BC%2Asin%28%22ACB%22%29%22%22=%22%22AB%2Asin%28%22BAC%22%29

sin%28%22ACB%22%29%22%22=%22%22AB%2Asin%28%22BAC%22%29%2FBC

sin%28%22ACB%22%29%22%22=%22%228%2Asin%28%2232%B0%22%29%2F5

sin%28%22ACB%22%29%22%22=%22%228%2Asin%28%2232%B0%22%29%2F5

sin%28%22ACB%22%29%22%22=%22%220.8478708228

Acute angles are QI angles and obtuse angles are
QII angles.  Since QI and QII angles have positive 
sines, there are two solutions for ∠ACB:

The acute angle C = ∠ACB can be found by using the 
inverse sine function on the calculator.  The
green acute angle is

∠ACB = 57.98083803°

The black obtuse angle indicated by the red arc that has 
that same sine can be found by subtracting the green one
from 180°, for the green one is its referent angle.

∠ACB = 180° - 57.98083803° = 122.019162°

Edwin