Two opposite sides of a parallelogram each have a length of 2 . If one corner of the parallelogram has an angle of (7 pi)/8  and the parallelogram's area is 3 , how long are the other two sides?

Aug 7, 2016

$= 3.92$

Explanation:

Area $= 3 = a b \sin \theta$ where $a = 2$ and $\theta = 7 \frac{\pi}{8}$ ;we have to find b=?
$3 = 2 b \sin \left(7 \frac{\pi}{8}\right)$
or
$b \sin \left(7 \frac{\pi}{8}\right) = \frac{3}{2}$
or
$b \left(0.383\right) = 1.5$
or
$b = \frac{1.5}{0.383}$
or
$b = 3.92$