Question

How do you use the law of cosines or law of sines if you are given a = 5, b = 8, c = 12?

Answer 1

First, use the law of cos to find cos A: `c^2 = a^2 + b^2 - 2ab.cos C`

144 = 64 + 25 - 80.cos C
`cos C = -55/80 = -0.69 -> C = 133.63.`deg
Calculator gives: sin C = 0.72

Next use the law of sin to find sin B: `sin B/b = sin C/c`

`sin B = (b.sin C)/c = (8(0.72))/12 = 0.48 --> B = 28.69`

`A = 180 - 133.63 - 28.69 = 17.68`