SOLUTION: Angle A is 80 degrees. Side AC is 14 and side Bc is 31. What are measures of angles b and c, and the AB.

Algebra ->  Triangles -> SOLUTION: Angle A is 80 degrees. Side AC is 14 and side Bc is 31. What are measures of angles b and c, and the AB.       Log On


   

Question 1103180: Angle A is 80 degrees. Side AC is 14 and side Bc is 31. What are measures of angles b and c, and the AB.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
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Use the law of sines,
sin%2880%29%2F31=sin%28b%29%2F14
sin%28b%29=%2814%2F31%29sin%2880%29
Solve for b.
Once you have b, solve for c.
80%2Bb%2Bc=180
c=100-b
Then use the law of sines again,
sin%2880%29%2F31=sin%28c%29%2FAB
AB%2Asin%2880%29=31sin%28c%29
AB=31%2A%28sin%28c%29%2Fsin%2880%29%29