# A triangle has sides A, B, and C. Sides A and B are of lengths 4 and 9, respectively, and the angle between A and B is (5pi)/8 . What is the length of side C?

Mar 13, 2018

$c = 11.2$

#### Explanation:

Well, this is a classic use of the cosine rule

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

${c}^{2} = {\left(4\right)}^{2} + {\left(9\right)}^{2} - 2 \left(4\right) \left(9\right) \cos \left(\frac{5 \pi}{8}\right)$

${c}^{2} = 16 + 81 - 72 \left(- 0.382683\right)$

${c}^{2} = 124.553$

$c = \sqrt{124.553}$

$c = 11.2$