# A triangle has sides A, B, and C. Sides A and B are of lengths 4 and 8, respectively, and the angle between A and B is pi/3. What is the length of side C?

Jan 25, 2016

$c = 4 \sqrt{3}$

#### Explanation:

The formula to be used is $\cos C = \frac{{a}^{2} + {b}^{2} - {c}^{2}}{2 a b}$

Given information is a=4, b=8 angle C= $\frac{\pi}{3}$

Accordingly $\frac{1}{2} = \frac{16 + 64 - {c}^{2}}{64}$

$32 = 80 - {c}^{2}$

${c}^{2} = 48$

$c = 4 \sqrt{3}$