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

Dec 31, 2017

$c \approx 7.475$

#### Explanation:

From the Law of Cosines we know that:

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

Solving for $c$ we have:

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

Substituting we have:

$c = \sqrt{{5}^{2} + {7}^{2} - 2 \left(5\right) \left(7\right) \cos \left(\frac{5 \pi}{12}\right)} \approx 7.475$