# A triangle has sides A, B, and C. Sides A and B are of lengths 5 and 2, respectively, and the angle between A and B is (7pi)/12 . What is the length of side C?

Oct 17, 2016

$c \approx 5.85$

#### Explanation:

Given:

$a = 5$
$b = 2$
$\angle C = \frac{7 \pi}{12}$

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

${c}^{2} = {5}^{2} + {2}^{2} - 2 \left(5\right) \left(2\right) \cos \left(\frac{7 \pi}{12}\right)$

$c \approx 5.85$