SOLUTION: Find the area of the given triangle: angle B = 20o angle C = 115o C = 16

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Question 43275: Find the area of the given triangle:
angle B = 20o
angle C = 115o
C = 16
Answer by psbhowmick(489) About Me  (Show Source):
You can put this solution on YOUR website!
At first use sine rule.
b%2Fsin%28B%29+=+c%2Fsin%28C%29
or b%2Fsin%2820%5Eo%29+=+16%2Fsin%28115%5Eo%29
or b+=+16%2Asin%2820%5Eo%29%2Fsin%28115%5Eo%29
or b+=+16%2Asin%2820%5Eo%29%2Fsin%28180%5Eo+-+65%5Eo%29
or b+=+16%2Asin%2820%5Eo%29%2Fsin%2865%5Eo%29
or b+=+16%2A0.342%2F0.906
or b+=+6.038

Now, in triangle ABC sum of the internal angles = 180%5Eo.
So, A+%2B+B+%2B+C+=+180%5Eo
or A+%2B+20%5Eo+%2B+115%5Eo+=+180%5Eo
or A+=+180%5Eo+-+20%5Eo+-+115%5Eo
or A+=+45%5Eo

Now, area of triangle ABC is %281%2F2%29b%2Ac%2Asin%28A%29 = %281%2F2%296.038%2A16%2Asin%2845%5Eo%29 = 34.156 sq units.