# A triangle has sides A, B, and C. Sides A and B are of lengths 12 and 11, respectively, and the angle between A and B is (11pi)/12 . What is the length of side C?

Jun 21, 2018

color(crimson)(c = 22.8 " units"

#### Explanation:

$a = 12 , b = 11 , \hat{C} = \frac{11 \pi}{12}$

Applying the Law of Cosines,

$c = \sqrt{{a}^{2} + {b}^{2} - 2 a b \cos C}$

c = sqrt(12^2 + 11^2 - (2 * 12 * 11 * cos ((11pi)/12)

color(crimson)(c = 22.8 " units"