# A triangle has sides A, B, and C. The angle between sides A and B is (5pi)/6 and the angle between sides B and C is pi/12. If side B has a length of 17, what is the area of the triangle?

$\frac{289}{4}$
This triangle is a isosceles triangle because the angle between sides A and C is $\frac{\pi}{12}$ too. 【$\pi$-($5 \pi$$/ 6$+$\frac{\pi}{12}$)=$\frac{\pi}{12}$
The area of the triangle $S$ is given as below:
$S$ =$\frac{1}{2}$$a b \sin C$
Now put $a = b = 17$ and C=5π$/ 6$ to get the answer.