# 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 11, what is the area of the triangle?

Jun 17, 2018

The area is given by $A = \frac{121}{2} \cdot {\left(\frac{1 + \sqrt{3}}{2 \cdot \sqrt{2}}\right)}^{2}$

#### Explanation:

The third angle is
$\frac{\pi}{2}$
So we have
$A = \frac{1}{2} a c$
and from

$\sin \left(\frac{\pi}{12}\right) = \frac{a}{11}$
$\sin \left(5 \cdot \frac{\pi}{12}\right) = \frac{c}{11}$
and
$\sin \left(\frac{\pi}{12}\right) = \sin \left(5 \frac{\pi}{12}\right) = \frac{1 + \sqrt{3}}{2 \cdot \sqrt{2}}$