SOLUTION: how would I find the measurement of the sides of a triangle if I had the measurements of the angles and the measurement of the perimeter. the perimiter is a set number (240)

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Question 892409: how would I find the measurement of the sides of a triangle if I had the measurements of the angles and the measurement of the perimeter. the perimiter is a set number (240)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You can use the law of sines.
Let the three angles be A,B and C.
Let the three corresponding sides be a,b, and c.
You know,
a%2Bb%2Bc=240
From the law of sines you know,
sin%28A%29%2Fa=sin%28B%29%2Fb=sin%28C%29%2Fc
So then from this,
b%2Asin%28A%29=a%2Asin%28B%29
b=a%28sin%28B%29%2Fsin%28A%29%29
and
c%2Asin%28A%29=a%2Asin%28C%29
c=a%28sin%28C%29%2Fsin%28A%29%29
Substituting,
a%2Ba%28sin%28B%29%2Fsin%28A%29%29%2Ba%28sin%28C%29%2Fsin%28A%29%29=240
a%281%2Bsin%28B%29%2Fsin%28A%29%2Bsin%28C%29%2Fsin%28A%29%29=240
Then you find a and work backwards to find b and c.