# A triangle has sides A, B, and C. Sides A and B are of lengths 5 and 2, respectively, and the angle between A and B is (11pi)/12 . What is the length of side C?

Dec 19, 2015

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

The angle between sides $a$ and $b$ will be angle $C$.

Plug in what you know.

${c}^{2} = {5}^{2} + {2}^{2} - 2 \left(2\right) \left(5\right) \cos \left(\frac{11 \pi}{12}\right)$

Thus, this can be simplified and plugged into a calculator (remember to be in radian mode.

$\text{side}$ $c = \sqrt{29 - 20 \cos \left(\frac{11 \pi}{12}\right)}$