# A triangle has sides A, B, and C. Sides A and B are of lengths 2 and 1, respectively, and the angle between A and B is (7pi)/8 . What is the length of side C?

side $c = 2.95 \text{ }$units

#### Explanation:

Given
side $a = 2$ and side $b = 1$ and angle $C = \frac{7 \pi}{8}$

by Cosine Law for sides

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

$c = \sqrt{{2}^{2} + {1}^{2} - 2 \cdot \left(2\right) \cdot \left(1\right) \cdot \cos \left(\frac{7 \pi}{8}\right)}$

$c = 2.9488163947668 \text{ }$units

God bless...I hope the explanation is useful.