# A triangle has sides A, B, and C. Sides A and B are of lengths 6 and 1, respectively, and the angle between A and B is (7pi)/8 . What is the length of side C?

Feb 8, 2016

$C \approx 6.93$

#### Explanation:

You can use the law of cosines here.

Let the angle opposite to side $A$ be $\alpha$, the angle opposite to side $B$ be $\beta$ and the angle opposite to side $C$ be $\gamma$.

Then the law of cosines states:

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

$= {6}^{2} + {1}^{2} - 2 \cdot 6 \cdot 1 \cos \left(\frac{7 \pi}{8}\right)$

$= 37 - 12 \cos \left(\frac{7 \pi}{8}\right)$

$\approx 37 - 12 \cdot \left(- 0.92\right)$

$\approx 48.09 {\text{ units}}^{2}$

Thus,

$C \approx 6.93 \text{ units}$