# A triangle has sides A, B, and C. Sides A and B are of lengths 7 and 8, respectively, and the angle between A and B is (7pi)/12 . What is the length of side C?

Length of side C is $11.92 \left(2 \mathrm{dp}\right)$ unit
Sides A=7 ;B=8 ; /_c=(7pi)/12=(7*180)/12=105^0
Applying Cosine law we get ${C}^{2} = \left({A}^{2} + {B}^{2} - 2 \cdot A \cdot B \cdot \cos c\right) \mathmr{and} {C}^{2} = \left({7}^{2} + {8}^{2} - 2 \cdot 7 \cdot 8 \cdot \cos 105\right) \mathmr{and} C = \sqrt{{7}^{2} + {8}^{2} - 2 \cdot 7 \cdot 8 \cdot \cos 105} = 11.92 \left(2 \mathrm{dp}\right)$unit [Ans]