# A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 3, respectively. The angle between A and C is (11pi)/24 and the angle between B and C is  (pi)/24. What is the area of the triangle?

Area of the triangle is $3$ $u n i {t}^{2}$
The angle between sides A & C is $\angle B = 11 \cdot \frac{\pi}{24} = {82.5}^{0}$
The angle between sides B & C is $\angle A = \frac{\pi}{24} = {7.5}^{0}$
The angle between sides A& B is $\angle C = 180 - \left(82.5 + 7.5\right) = {90}^{0}$
This is a right angled triangle whose base is side A and altitude is side B $\therefore$ Area $= \frac{1}{2} \cdot A \cdot B = \frac{1}{2} \cdot 2 \cdot 3 = 3$ $u n i {t}^{2}$[Ans]