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

Nov 6, 2016

$\text{C} = 15.7$

#### Explanation:

To answer this question, we have to use the law of cosines.

"C"^2="A"^2+"B"^2-2"AB"cos("c")=81+49-126cos(7/8pi) =246.4

$\text{C} = \sqrt{264.4} = 15.7$

Nov 6, 2016

Cosine rule (rearranged for c) = ${c}^{2} = {a}^{2} + {b}^{2} - 2 a b \cdot \cos C$
$= c = \sqrt{{9}^{2} + {7}^{2} - 2 \cdot 9 \cdot 7 \cdot \cos \left(\frac{7 \pi}{8}\right)}$