# A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 20, respectively. The angle between A and C is (17pi)/24 and the angle between B and C is  (pi)/8. What is the area of the triangle?

Dec 16, 2015

22.96 (approx) sq units

#### Explanation:

Sides are marked with small letters. So the sides are a,b,c. Triangle is ABC. Side opposite A is a, side opposite B is b...... The triangle is like this

The area of the triangle would be $\frac{1}{2} a b \sin C$

=$\frac{1}{2} 120 \sin \left(\frac{\pi}{8}\right)$ = 60(0.3826)=22.96 (approx).

For exact value write $\cos \left(\frac{\pi}{4}\right) = 1 - 2 {\sin}^{2} \left(\frac{\pi}{8}\right)$, that is

$\frac{1}{\sqrt{2}} = 1 - 2 {\sin}^{2} \left(\frac{\pi}{8}\right)$. Simplify for $\sin \left(\frac{\pi}{8}\right)$ and plug in the Area expression $60 \sin \left(\frac{\pi}{8}\right)$