# 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 (11pi)/12 . What is the length of side C?

Mar 25, 2018

color(indigo)("Length of side c " = sqrt(a^2 + b^2 - (2 a b cos C)) ~~ 12.89

#### Explanation:

$G i v e n : a = 5 , b = 8 , \hat{C} = \frac{11 \pi}{12} , \text{To find side c}$.

Applying cosine law,

$c = \sqrt{{a}^{2} + {b}^{2} - \left(2 a b \cos C\right)}$

c = sqrt(5^2 n+ 8^2 - (2 * 5 * 8 * cos ((11pi)/12)

color(indigo)("Length of side c " = sqrt(25 + 64 - 80 cos ((11pi)/12)) ~~ 12.89