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

Jul 23, 2018

The side $c = 9.6 u$

#### Explanation:

Apply the cosine rule

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

The sides are

$a = 7$

$b = 5$

And

$\hat{C} = \frac{7}{12} \pi$

Therefore,

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

${c}^{2} = 92.12$

$c = \sqrt{92.12} = 9.6 u$