SOLUTION: Two side of a triangle are 50m and 60m long. The angle included between these sides are 30 degrees, what is the interior angle opposite the longest side?

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Question 992778: Two side of a triangle are 50m and 60m long. The angle included between these sides are 30 degrees, what is the interior angle opposite the longest side?
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Let us use the cosine rule first.
a = 50
b = 60
C = 30 degrees

c%5E2+=+a%5E2+%2B+b%5E2+-+2abcos%28C%29
c%5E2+=+50%5E2+%2B+60%5E2+-+2%2A50%2A60%2Acos%2830%29+=+903.8476
c+=+30.06

So largest side is b = 60 m.

Using Sine rule
c%2Fsin%28C%29+=+b%2Fsin%28B%29
sin%28B%29+=+%28b%2Asin%28C%29%29%2Fc
sin%28B%29+=+%2860%2Asin%2830%29%29%2F30.06
B = 86.3 degree