Question

Two opposite sides of a parallelogram each have a length of `5`. If one corner of the parallelogram has an angle of `(5 pi)/8` and the parallelogram's area is `15`, how long are the other two sides?

Answer 1

The other two side are long `~=3.25`

Explanation:

You can use the inverse of the following formula, related to the area of a triangle, that would be an half of the given parallelogram, containing the angle of `(5pi)/8`:

`Area=1/2 a*b*sin hat (ab)`

Then let's subsitute `a=5` and `Area=15/2` and solve `b`:

`cancel15^3/cancel2=1/cancel2*cancel5*b*sin((5pi)/8)`

`b=3/sin((5pi)/8)~=3.25`