# A triangle has sides A, B, and C. Sides A and B are of lengths 8 and 1, respectively, and the angle between A and B is (5pi)/8 . What is the length of side C?

Jan 27, 2018

$C = 8.4334$

#### Explanation:

We have two lengths and the angle between them. As such, to determine length C (the opposite length) we must use the law of cosines, in our case that will be:

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

where $x$ is the angle made between $A$ and $B$.

Plugging in the numbers gives us:

${C}^{2} = {8}^{2} + {1}^{2} - 2 \left(8\right) \left(1\right) \cos \left(\frac{5 \pi}{8}\right)$

$= 65 - 16 \left(- 0.382683\right)$

$= 65 + 6.12293 = 71.1229$

So:

${C}^{2} = 71.1229$

$\therefore C = \sqrt{71.1229} = 8.4334$