Question

Two opposite sides of a parallelogram each have a length of `8`. If one corner of the parallelogram has an angle of `(3pi)/8` and the parallelogram's area is `24`, how long are the other two sides?

Answer 1

`l~~3.2471766`

Explanation:

First, we determinate the hight of the parallelogram.
`A=g*h_g|:g`
`A/g=h_g`
`24/8=h_g=3`
Now we use the sine of the known angle.
`sin(alpha)=("opposite side")/("hypotenuse")|*"hypotenuse"/sin(alpha)`
`"hypotenuse"=("opposite side")/(sin(alpha))`
`"hypotenuse"=3/sin(3*pi/8)~~3.2471766`