# Two opposite sides of a parallelogram each have a length of 32 . If one corner of the parallelogram has an angle of (5 pi)/12  and the parallelogram's area is 160 , how long are the other two sides?

Aug 27, 2016

$= 4.83$

#### Explanation:

Area of Parallelogram $= 160 = a b \sin \theta$ where $a = 32$ and b=? and $\theta = \frac{5 \pi}{12}$
or
$160 = 32 \times b \times \sin \left(\frac{5 \pi}{12}\right)$
or

$b = \frac{160}{32} \times \left(0.966\right)$

or

$b = 5 \times \left(0.966\right)$

or

$b = 4.83$