# If sides A and B of a triangle have lengths of 4 and 6 respectively, and the angle between them is pi/3, then what is the area of the triangle?

Jun 1, 2018

$6 \cdot \sqrt{3}$

#### Explanation:

We use the formula
$A = \frac{1}{2} \cdot a \cdot b \cdot \sin \left(\gamma\right)$
and
$\sin \left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}$

so

$A = \frac{1}{2} \cdot 6 \cdot 4 \cdot \sin \left(\frac{\pi}{3}\right)$
$A = 6 \cdot \sqrt{3}$