SOLUTION: Determine the measure of side a given the following informaiton for triangle ABC: C=25degrees, B=108degrees, c=59ft

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Question 87186: Determine the measure of side a given the following informaiton for triangle ABC: C=25degrees, B=108degrees, c=59ft
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

Determine the measure of side a given the 
following informaiton for triangle ABC: 
C = 25degrees, B = 108degrees, c = 59ft


First we find angle A using

A + B + C = 180°

A + 108° + 25° = 180°

A + 133° = 180°

A = 47°



Now we use the law of sines:

a%2Fsin%28A%29 = b%2Fcos%28B%29 = c%2Fsin%28C%29

We only need

a%2Fsin%28A%29 = c%2Fsin%28C%29

Solve for c:

Cross multiply:

a%2Asin%28C%29 = c%2Asin%28A%29

Divide both sides by sin%28C%29

a = %28c%2Asin%28A%29%29%2Fsin%28C%29 

     59*sin(47°)
a = -------------
       sin(25°)

a = 102.1012869 ft.

Since the angles are measured to the 
nearest degree, and the side c measured to
2 significant digits, then side a
should be rounded to either 102 ft. or 100 ft. 

Edwin