# 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 (7pi)/24 and the angle between B and C is  (5pi)/8. What is the area of the triangle?

Area of the triangle is $0.78$ units
/_B =7*180/24=52.5^0 ; /_A=5*180/8=112.5^0 :./_C=180-(52.5+112.5)=15^0 Now he two sides of the triangle A B and their included angle are $2 , 3 \mathmr{and} {15}^{0}$ Hence the Area of the triangle is $\frac{A \cdot B \cdot \sin \left(C\right)}{2} = \frac{2 \cdot 3 \cdot 26}{2} = 0.78$ Units[Ans]