# A triangle has sides A, B, and C. Sides A and B are of lengths 2 and 5, respectively, and the angle between A and B is pi/6. What is the length of side C?

Feb 25, 2018

Length of third side $\textcolor{\in \mathrm{di} g o}{c = 3}$

#### Explanation:

$\textcolor{w h i t e}{a a a a a a a a a a}$ Law of Cosines

$c = \sqrt{{a}^{2} + {b}^{2} - \left(2 a b \cos C\right)}$

=> sqrt((2^2 + 5^2 - (2 * 2 * 5 * cos (pi/6))

Length of third side $\textcolor{\in \mathrm{di} g o}{c = 3}$