# A triangle has sides A, B, and C. Sides A and B are of lengths 5 and 8, respectively, and the angle between A and B is pi/3. What is the length of side C?

Sep 13, 2017

The length of side $C$ is $7$ unit.

#### Explanation:

Sides of triangle are $A = 5 , B = 8$

The angle between $A \mathmr{and} B$ is $\angle c = \frac{\pi}{3} = \frac{180}{3} = {60}^{0}$

Applying cosine law we can find $C$

$C = \sqrt{{A}^{2} + {B}^{2} - 2 A B \cos c}$ or

$C = \sqrt{{5}^{2} + {8}^{2} - 2 \cdot 5 \cdot 8 \cos 60}$ or

$C = \sqrt{25 + 64 - 80 \cdot \frac{1}{2}}$ or

$C = \sqrt{25 + 64 - 40} = \sqrt{49} = 7$ unit

The length of side $C$ is $7$ unit . [Ans]