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

a=12 b=13 c=5
b2 = a2 + c2
169 = 144 + 25

So angle B is 90 degrees

By the law of sines

sin(A)/a = sin (B)/b = sin(C)/c

or sin(A)/a = sin(90)/b
or sin(A) = a/b = 12/13
or A = 67.37 degrees

so angle C = 180 - (90 + 67.37) = 22.63 degrees

Answer 2

use the cosines law

a^2 = b^2 + c^2 - 2bc cos A

cos A = -(a^2 - b^2 - c^2) / 2bc etc.

cos A = -(12^2 - 13^2 - 5^2) / 2*13*5 = 0.38
A = 67.67