Question

Two opposite sides of a parallelogram each have a length of `4`. If one corner of the parallelogram has an angle of `(7 pi)/8` and the parallelogram's area is `18`, how long are the other two sides?

Answer 1

`11.76` each

Explanation:

The area is `A = b xx h`, so select one of the known sides as the base. Then `h = 18/4 = 4.5`

The angle between an unknown side and the base (4) is the complement of `7/8pi, or 1/8pi`.
The unknown side is thus
`x = h/(sin(pi/8))` ; `x = 4.5/0.383 = 11.76`

You can check it by using this number, and working it again from the other angle (`pi/8`) to see that you get the length of 4 back for the short sides.