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

Mar 11, 2016

see below

#### Explanation:

${C}^{2} = {A}^{2} + {B}^{2} - 2 A B \cos \theta$,where $\theta = \frac{\pi}{8}$=angle between A and B
$C = \sqrt{{A}^{2} + {B}^{2} - 2 A B \cos \theta} = \sqrt{{7}^{2} + {9}^{2} - 2 \times 7 \times 9 \times \cos \left(\frac{\pi}{8}\right)}$
=>sqrt(7^2+9^2-2xx7xx9xxsqrt(1/2(1+cos(pi/4))

pl complete the calculation