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

Feb 24, 2018

Length of side $c = \textcolor{b l u e}{7.76}$

#### Explanation:

Given $a = 7 , b = 2 , \hat{C} = \left(\frac{7 \pi}{12}\right)$

To find length of side $c$

Applying cosine law,

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

$\implies = \sqrt{{7}^{2} + {2}^{2} - \left(2 \cdot 7 \cdot 2 \cos \left(\frac{7 \pi}{12}\right)\right)} = \textcolor{b l u e}{7.76}$