# If sides A and B of a triangle have lengths of 9 and 12 respectively, and the angle between them is (pi)/3, then what is the area of the triangle?

Dec 18, 2015

$27 \sqrt{3}$

#### Explanation:

Taking a look at the triangle, we have something like the following:

From the right triangle containing the angle $\frac{\pi}{3}$ we have

$\sin \left(\frac{\pi}{3}\right) = \frac{h}{9} \implies h = 9 \sin \left(\frac{\pi}{3}\right) = \frac{9 \sqrt{3}}{2}$

Then, applying the area formula $A = \frac{1}{2} b h$

$\text{area} = \frac{1}{2} \left(12\right) \left(\frac{9 \sqrt{3}}{2}\right) = 27 \sqrt{3}$