# 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 (3pi)/8 and the angle between B and C is  (5pi)/12. What is the area of the triangle?

Apr 10, 2017

The area of the triangle is $0.91 \left(2 \mathrm{dp}\right)$ sq.unit

#### Explanation:

The angle between sides A and C is $\angle b = \frac{3 \pi}{8} = \frac{3 \cdot 180}{8} = {67.5}^{0}$
The angle between sides B and C is $\angle a = \frac{5 \pi}{12} = \frac{5 \cdot 180}{12} = {75}^{0}$
The angle between sides A and B is $\angle c = 180 - \left(67.5 + 75\right) = {37.5}^{0}$

So , the two sides and their included angle is known as $A = 3 , B = 1 , \angle c = {37.5}^{0}$

The area of the triangle is ${A}_{t} = \frac{A \cdot B \cdot \sin c}{2} = \frac{3 \cdot 1 \cdot \sin 37.5}{2} \approx 0.91 \left(2 \mathrm{dp}\right)$ sq.unit [Ans]