# A triangle has sides A, B, and C. Sides A and B are of lengths 2 and 7, respectively, and the angle between A and B is (7pi)/8 . What is the length of side C?

Jun 30, 2016

Given
$\text{Side A"=2,"Side B} = 7$

theta="Angle between" A & B=(7pi)/8
"Side C"= ?

We know

${C}^{2} = {A}^{2} + {B}^{2} - 2 A B \cos \theta$

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

$\implies C = \sqrt{{2}^{2} + {7}^{2} - 2 \cdot 2 \cdot 7 \cdot \cos \left(7 \frac{\pi}{8}\right)}$

$\implies C \approx 8.88$