missing angles?

Question

given a=12 b=13 c=5

have to find alpha, beta, gamma

please help me, I don't know how to do this without any angles given!! It you could show me step by step what you did, so I can follow along that would be great!! thanks

Answer 1

You should recognize this as a Pythagorean triple:
13^2 = 5^2 + 12^2
169 = 25 + 144
Therefore angel B is a right angle.
Then:
A = arc tan (12/5) = 67.38degrees
And:
C = arc tan(5/12) = 22.62degrees

Answer 2

You must use the law of cosines:

a^2 = b^2 + c^2 - 2bc*cos(α)

I think you can get it from here.