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 23, what is the area of the triangle?

May 5, 2017

This is a right triangle with hypotenuse $B = 23$

Explanation:

The area is

$\frac{1}{2} \left(23 \sin \left(\frac{\pi}{12}\right)\right) \left(23 \cos \left(\frac{\pi}{12}\right)\right) = \frac{529}{2} \left(\sin \left(\frac{\pi}{12}\right) \cos \left(\frac{\pi}{12}\right)\right)$

$= \frac{529}{2} \left(\frac{1}{2} \sin \left(\frac{2 \pi}{12}\right)\right)$

$= \frac{529}{4} \left(\sin \left(\frac{\pi}{6}\right)\right)$

$= \frac{529}{8}$