# A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 1, respectively. The angle between A and C is (13pi)/24 and the angle between B and C is  (3pi)/8. What is the area of the triangle?

Mar 5, 2017

the area is $\frac{\sqrt{6} - \sqrt{2}}{4}$

#### Explanation:

The angle between A and B is:

$\hat{A B} = \pi - \frac{13}{24} \pi - \frac{3}{8} \pi = \frac{2}{24} \pi = \frac{1}{12} \pi$

The area of the triangle is:

$\frac{1}{2} A \cdot B \cdot \sin \left(\hat{A B}\right) = \frac{1}{\cancel{2}} \cdot \cancel{2} \cdot 1 \cdot \sin \left(\frac{\pi}{12}\right)$

$\frac{\sqrt{6} - \sqrt{2}}{4}$