# A triangle has sides A, B, and C. Sides A and B are of lengths 2 and 3, respectively, and the angle between A and B is (pi)/8 . What is the length of side C?

The length of side $C$ is $1.38 \left(2 \mathrm{dp}\right) u n i t$
Here the sides A=2 ; B=3 and their included angle $c = \frac{\pi}{8} = \frac{180}{8} = {22.5}^{0}$ are known.
Applying cosine law we get $C = \sqrt{{A}^{2} + {B}^{2} - 2 \cdot A \cdot B \cdot \cos c} \mathmr{and} C = \sqrt{{2}^{2} + {3}^{2} - 2 \cdot 2 \cdot 3 \cdot \cos 22.5} = 1.38 \left(2 \mathrm{dp}\right) u n i t$[Ans]