# A triangle has sides A, B, and C. Sides A and B have lengths of 3 and 1, respectively. The angle between A and C is (5pi)/24 and the angle between B and C is  (pi)/24. What is the area of the triangle?

Area of the triangle is $1.06 s q . u n i t$
The angle between sides A & C is $\angle b = 5 \cdot \frac{180}{24} = {37.5}^{0}$
The angle between sides B & C is $\angle a = \frac{180}{24} = {7.5}^{0}$
The included angle between sides A & B is $\angle c = 180 - \left(37.5 + 7.5\right) = {135}^{0}$ So we have A=3 ; B=1  and included angle between them is ${135}^{0}$. Area of the triangle is ${A}_{t} = \frac{1}{2} \cdot a \cdot b \cdot \sin c = \frac{1}{2} \cdot 3 \cdot 1 \cdot \sin 135 = \frac{3}{2} \cdot 0.707 = 1.06 s q . u n i t$[Ans]