# A triangle has sides A, B, and C. Sides A and B are of lengths 2 and 12, respectively, and the angle between A and B is (7pi)/12 . What is the length of side C?

Jan 27, 2018

$c \approx 12.666$

#### Explanation:

Given $a = 2$, $b = 12$, and $C = \frac{7 \pi}{12}$, we can calculate side $c$ using the Law of Cosines:

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

$c = \sqrt{{2}^{2} + {12}^{2} - 2 \left(2\right) \left(12\right) \cos \left(\frac{7 \pi}{12}\right)}$

$c \approx 12.666$