# A triangle has sides A, B, and C. If the angle between sides A and B is (pi)/6, the angle between sides B and C is (3pi)/4, and the length of side B is 3, what is the area of the triangle?

Aug 18, 2016

Area of the triangle is $6.15 \left(2 \mathrm{dp}\right)$ sq.unit.

#### Explanation:

The angle between sides A and B is $\angle c = \frac{\pi}{6} = {30}^{0}$
The angle between sides B and C is $\angle a = 3 \cdot \frac{\pi}{4} = {135}^{0}$
The angle between sides C and A is /_b= (180-(30+135)=15^0
Using sine law we get $\frac{A}{\sin} a = \frac{B}{\sin} b \mathmr{and} A = 3 \cdot \left(\sin \frac{135}{\sin} 15\right) = 8.2$
Now we know two sides A & B and their included angle$\angle c \therefore$
Area of the triangle is${A}_{t} = \frac{A \cdot B \cdot \sin c}{2} = \frac{8.2 \cdot 3 \cdot \sin 30}{2} = 6.15 \left(2 \mathrm{dp}\right)$sq.unit[Ans]