# A triangle has sides A, B, and C. Sides A and B are of lengths 8 and 7, respectively, and the angle between A and B is (5pi)/12 . What is the length of side C?

Jul 16, 2018

$\sqrt{113 - 28 \cdot \sqrt{2} \cdot \left(\sqrt{3} - 1\right)}$

#### Explanation:

Using the Theorem of cosines:

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

$\cos \left(5 \cdot \frac{\pi}{12}\right) = \frac{\sqrt{3} - 1}{2 \sqrt{2}}$
we get

$c = \sqrt{113 - 28 \cdot \sqrt{2} \left(\sqrt{3} - 1\right)}$