# If sides A and B of a triangle have lengths of 12 and 8 respectively, and the angle between them is (5pi)/6, then what is the area of the triangle?

Area of triangle color(green)(A_t = 24 sq units
Given : $a = 12 , b = 8 , \hat{C} = \frac{5 \pi}{6}$
Formula for area of triangle ${A}_{t} = \left(\frac{1}{2}\right) a b \sin C$
${A}_{t} = \left(\frac{1}{2}\right) \cdot 12 \cdot 8 \cdot \sin \left(\frac{5 \pi}{6}\right) = 24$ sq units