# How do you solve a triangle given a = 8, c = 12, and B = 72?

Nov 8, 2015

Law of sine and cosine

#### Explanation:

You first need to fine the missing side, in this case it would be 'b.'

Use this equation: ${b}^{2} = {a}^{2} + {c}^{2} - 2 a c \sin b$

You will have the side b and can use the the same equation, just manipulated to find the other angle.

That equation is: $\frac{- {a}^{2} + {b}^{2} + {c}^{2}}{2 b c} = \sin A$

That will give you the angle of angle A. Since you have 2 angles of the triangle you can easily find the third, simply subtracting the sum of both angles from 180.