# A triangle has sides A, B, and C. Sides A and B are of lengths 9 and 17, respectively, and the angle between A and B is (7pi)/8 . What is the length of side C?

Jul 20, 2016

$C \cong 25.5483$.

#### Explanation:

We use Cosine-Rule, which, in our case, states that,

${C}^{2} = {A}^{2} + {B}^{2} - 2 A B \cos \left(\angle \left(A , B\right)\right)$

$= 81 + 289 - 2 \times 9 \times 17 \cos \left(7 \frac{\pi}{8}\right)$

$= 370 - 306 \cos \left(\pi - \frac{\pi}{8}\right)$

$= 370 - 306 \left(- \cos \frac{\pi}{8}\right) \ldots \ldots \ldots \ldots \ldots \ldots \ldots \left[\cos \left(\pi - \theta\right) = - \cos \theta\right]$

$370 + 306 \cos \left({22}^{\circ} 30 '\right)$

$370 + 306 \left(0.9239\right)$

$370 + 282.7134 = 652.7134$

$\therefore C = \sqrt{652.7134} \cong 25.5483$.