# A triangle has sides A, B, and C. Sides A and B are of lengths 4 and 1, respectively, and the angle between A and B is (2pi)/3 . What is the length of side C?

Nov 29, 2016

Based on the theorem of cosine the length of the $C$ is given by:

${C}^{2} = {A}^{2} + {B}^{2} - 2 A B \cos \left(A \angle B\right)$

#### Explanation:

So:

$C = \sqrt{{4}^{2} + {1}^{2} - 2 \cdot 4 \cdot 1 \cdot \cos \left(\frac{2 \pi}{3}\right)}$

$C = \sqrt{17 - 8 \cdot \left(- \frac{1}{2}\right)} = \sqrt{21}$