# A triangle has sides A, B, and C. Sides A and B are of lengths 9 and 8, respectively, and the angle between A and B is pi/3. What is the length of side C?

Feb 11, 2018

The side C is 8.544

#### Explanation:

$S i \mathrm{de} A = 9$
$S i \mathrm{de} B = 8$
$C = \frac{\pi}{3}$
Side C
$= \sqrt{{A}^{2} + {B}^{2} - 2 A B \cos C}$
Substituting
=sqrt(9^2+8^2-(2)(9)(8)cos(pi/3)
=sqrt(81+64-(2)(72)(1/2)
sqrt(81+64-72
=sqrt(9+64
$= \sqrt{73}$
$= 8.544$
The side C is 8.544