# A triangle has sides A, B, and C. If the angle between sides A and B is (pi)/12, the angle between sides B and C is (pi)/2, and the length of B is 2, what is the area of the triangle?

May 23, 2017

Area of triangle is $0.54 \left(2 \mathrm{dp}\right)$ sq.unit.

#### Explanation:

The angle between sides $A \mathmr{and} B$ is $\angle c = \frac{\pi}{12} = \frac{180}{12} = {15}^{0}$

The angle between sides $B \mathmr{and} C$ is $\angle a = \frac{\pi}{2} = \frac{180}{2} = {90}^{0}$

The angle between sides $C \mathmr{and} A$ is $\angle b = 180 - \left(90 + 15\right) = {75}^{0}$

 B =2 ; Appliying sine law we can find $A$ as $\frac{A}{\sin} a = \frac{B}{\sin} b \mathmr{and} A = B \cdot \sin \frac{a}{\sin} b \mathmr{and} A = 2 \cdot \sin \frac{90}{\sin} 75 \approx 2.07$

Now we know sides $A \approx 2.07 \mathmr{and} B = 2$ and their included angle $\angle c = {15}^{0}$

Area of triangle ${A}_{t} = \frac{A \cdot B \cdot \sin c}{2} \approx \frac{2.07 \cdot 2 \cdot \sin 15}{2} \approx 0.54 \left(2 \mathrm{dp}\right)$ sq.unit [Ans]