# If sides A and B of a triangle have lengths of 5 and 7 respectively, and the angle between them is (5pi)/12, then what is the area of the triangle?

Oct 2, 2017

$16.90$

#### Explanation:

Using the formula
$a r e a = \frac{1}{2} a b \sin C$
where $C$ is the angle between the two sides $a$ and $b$.

$a r e a = \frac{1}{2} \left(5\right) \left(7\right) \sin \left(\frac{5 \pi}{12}\right)$

$= \frac{1}{2} \left(35\right) \sin \left(\frac{5 \pi}{12}\right)$

$= 17.5 \sin \left(\frac{5 \pi}{12}\right)$

$= 16.90$ to 2 s.f