# 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 33, what is the area of the triangle?

May 31, 2017

The area of triangle is $136.1 \left(1 \mathrm{dp}\right)$ sq.unit

#### Explanation:

The angle between sides $A \mathmr{and} B$ is $\angle c = \frac{5 \pi}{12} = \frac{5 \cdot 180}{12} = {75}^{0}$

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

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

Applying sine law we can find  A/sina=B/sinb ; B=33 :. A/sin15=33/sin90 or A= 33*sin 15~~8.54(2 dp); [sin 90 =1]

Now we know the adjacent sides $A , B$ and their included angle $\angle c$.

The area of triangle is ${A}_{t} = \frac{A \cdot B \cdot \sin c}{2} = \frac{8.54 \cdot 33 \cdot \sin 75}{2} \approx 136.1 \left(1 \mathrm{dp}\right)$ sq.unit