Question

Two opposite sides of a parallelogram each have a length of `32`. If one corner of the parallelogram has an angle of `(5 pi)/12` and the parallelogram's area is `140`, how long are the other two sides?

Answer 1

The other sides are (each) `4.53` units long

Explanation:

(Refer to the above diagram)

`sin((5pi)/12)=h/32`
`rarr h=32sin((5pi)/12)`

`Area = x * h`

Using the given value for the `Area`
`color(white)("XXX")140 = x * 32sin((5pi)/12)`

`color(white)("XXX")rarr x= 140/(32 sin((5pi)/12))~~4.53`