# A triangle has sides A, B, and C. Sides A and B are of lengths 7 and 4, respectively, and the angle between A and B is (7pi)/12 . What is the length of side C?

Here the sides a= 7 ; b=4 and their included angle is $C = 7 \cdot \frac{180}{12} = {105}^{0}$ We know
${c}^{2} = {a}^{2} + {b}^{2} - 2 \cdot a \cdot b \cdot \cos \left(C\right)$ or ${c}^{2} = {7}^{2} + {4}^{2} - 2 \cdot 7 \cdot 4 \cdot \cos \left(105\right)$
or ${c}^{2} = 49 + 16 - 56 \cdot \left(- 0.2588\right)$ or${c}^{2} = 79.49$ or $c = 8.91$[answer]