Question

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

Answer 1

b^2 = a^2 + c^2 - 2ac cos 54 = 1485
b = 38.5
Check your numbers again.

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

Answer 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...

Answer 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