# Two opposite sides of a parallelogram each have a length of 24 . If one corner of the parallelogram has an angle of (5 pi)/12  and the parallelogram's area is 120 , how long are the other two sides?

Feb 9, 2018

Other two sides are $\textcolor{g r e e n}{5.1764}$ each approx.

#### Explanation:

Area of parallelogram ${A}_{p} = b \cdot h = b \cdot a \sin \theta$

Given ${A}_{p} = 120 , \theta = \frac{5 \pi}{12} = {75}^{0} , b = 24$

To find a.

a = A_p / (b sin theta) = 120 / (24 * sin ((5pi)/12)) ~~ color(green)(5.1764