# Two opposite sides of a parallelogram each have a length of 9 . If one corner of the parallelogram has an angle of (2 pi)/3  and the parallelogram's area is 18 , how long are the other two sides?

Jul 8, 2017

$\text{Missing side} = 2.31$

#### Explanation:

${\left(\frac{2 \pi}{3}\right)}^{\text{c}} = {60}^{\circ}$

If the whole area is made of two equal triangles, and has an area of 18 in total, then the area of one triangle is $\frac{18}{2} = 9$

Area of a triangle $= \left(\frac{a \cdot b \cdot \sin \left(C\right)}{2}\right)$, where $a$ and $b$ are two sides, and $C$ is the angle directly opposite to the unknown side.

In this case, $\text{Area of triangle} = 9 = \frac{a \cdot 9 \cdot \sin \left(60\right)}{2}$, then $a = \frac{18}{9 \sin \left(60\right)} = \frac{2}{\sin} \left(60\right) = 2.31 \left(\text{rounded to 2 d.p.}\right)$