# Pre-Calculus

Solve the triangle. Round to the nearest tenth.

B=54deg a=42 c=6.5

1. I found length of b using law of cosine and got 36.2
2. Using side of b, I used the law of sine to get angle A = 28.2
3. I added B+A and subtracted from 180 to get angle C = 127.8 which DOES NOT make sense since side c is the smallest side. I can't seem to find my error. Help please?

Thanks

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1. b^2 = a^2 + c^2 - 2ac cos 54 = 1485
b = 38.5

I get sinA = a*sinB/b = .1366
A = 7.85 degrees

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2. I didn't get A = 7.85 degs...

I got 61.8deg for A this time... which would make C have 64.2deg which still doesn't make sense...

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3. You are correct; I inserted the wrong value of a in the law of sines. Sin A = 0.88256 and A = 62 degrees or 118 degrees. You have to choose the larger value. That means C = 180 - 118 - 54 = 8 degrees

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