# 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 8, what is the area of the triangle?

$A r e a = 8$ square units

#### Explanation:

Use $A r e a = \frac{1}{2} \cdot b \cdot h$

Compute height $h$. The altitude from angle $B$ to side $b$

$h = \frac{b}{\cot A + \cot C}$

$h = \frac{8}{\cot \left(\frac{\pi}{12}\right) + \cot \left(5 \frac{\pi}{12}\right)} = 2$

$h = 2$

Compute Area:

$A r e a = \frac{1}{2} \cdot 8 \cdot 2$

$A r e a = 8$