# A triangle has sides A, B, and C. Sides A and B are of lengths 7 and 12, respectively, and the angle between A and B is (5pi)/8 . What is the length of side C?

May 3, 2016

Length of side $C$ is $16.04$.

#### Explanation:

If two sides are $a$ and $b$ and included angle $\theta$, then the side opposite is given by

sqrt(a^2+b^2-2abcostheta

Hence, side $C$ is

sqrt(7^2+12^2-2xx7xx12xxcos((5pi)/8)

= $\sqrt{49 + 144 - 168 \times \left(- 0.3827\right)}$

= $\sqrt{193 - \left(- 64.2936\right)}$

= $\sqrt{193 + 64.2936}$

= $\sqrt{257.2936} = 16.04$