# A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 9, respectively. The angle between A and C is (3pi)/8 and the angle between B and C is  (5pi)/24. What is the area of the triangle?

May 21, 2016

30.43

#### Explanation:

I think the simplest way to think about the problem is to draw out a diagram.

The area of a triangle can be calculated using

$a \times b \times \sin c$

To calculate angle C, use the fact that angles in a triangle add up to 180$\circ$, or $\pi$.

Therefore, angle C is $\frac{5 \pi}{12}$ I have added this to the diagram in green.

Now we can calculate the area.

$\frac{1}{2} \times 7 \times 9 \times \sin \left(\frac{5 \pi}{12}\right)$ = $30.43$ units squared