Question

Two opposite sides of a parallelogram each have a length of `6`. If one corner of the parallelogram has an angle of `(5 pi)/12` and the parallelogram's area is `54`, how long are the other two sides?

Answer 1

Other two sides are `9.32` units.

Explanation:

Area of a parallelogram is given by `axxbxxsintheta`,

where `a` and `b` are two sides of a parallelogram and `theta` is the angle included between them.

As one side is `6`; included angle is `(5pi)/12` and area is `54` we have

`6xxbxxsin(5pi)/12=54` or `b=54/(6xxsin((5pi)/12))=9/0.9659=9.32`

Hence, other two sides are `9.32` units.