# A triangle has sides A, B, and C. Sides A and B are of lengths 4 and 2, respectively, and the angle between A and B is (3pi)/8 . What is the length of side C?

Oct 16, 2016

Side C is approximately $3.725$.

#### Explanation:

${c}^{2} = {a}^{2} + {b}^{2} - 2 a b \cos C$

where $a , b \mathmr{and} c$ are lengths of the sides of a triangle and $C$ is the measure of the angle between sides a and b.

${c}^{2} = {4}^{2} + {2}^{2} - 2 \left(4\right) \left(2\right) \cos \left(\frac{3 \pi}{8}\right)$

${c}^{2} = 16 + 4 - 16 \left(0.3827\right)$

${c}^{2} = 13.877$

$c = 3.725$