# A triangle has sides A, B, and C. The angle between sides A and B is (5pi)/12 and the angle between sides B and C is pi/12. If side B has a length of 10, what is the area of the triangle?

Hence Area of the right angled triangle is $12.5$ square units.
The angle between sides A and B is $\angle C = 5 \cdot \frac{180}{12} = {75}^{0}$
The angle between sides B and C is $\angle A = \frac{180}{12} = {15}^{0} \therefore \angle B = 180 - \left(75 + 15\right) = {90}^{0}$ Side $B = 10$ Applying sine law $\frac{A}{\sin} A = \frac{B}{\sin} B = \frac{C}{\sin} C$
we get $A = 10 \cdot \sin 15 = 2.588$ and $C = 10 \cdot \sin 75 = 9.659$ Hence Area of the right angled triangle is $= \frac{1}{2} \cdot 9.659 \cdot 2.588 = 12.5$ Square units.
Here, Base $= 9.659$ and Height $= 2.588$[Ans]