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.

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(20056) (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:



Cross-multiply











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

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