Question

Two opposite sides of a parallelogram each have a length of `18`. If one corner of the parallelogram has an angle of `(5 pi)/12` and the parallelogram's area is `120`, how long are the other two sides?

Answer 1

`~~6.97`

Explanation:

Consider the diagram

First of all we know that one of the side of the parallelogram has a length of `18`

The angle between the sides with length `18` and `b` is `75^circ((5pi)/12)`

We need to find `b`

We use the formula for the area of parallelogram (Trigonometry)

`color(blue)("Area of parallelogram"=a*b*sin(gamma)`

Where

`color(orange)("a and b are the adjacent sides"`

`color(orange)(gamma` `color(orange)("is the angle between them"`

`:.18*b*sin(75^circ)=120`

`rarrb*sin(75^circ)=120/18`

`rarrb*sin(75^circ)=20/3`

`rarrb*0.96=6.7`

`rarrb=6.7/0.96`

`color(green)(rArrb~~6.97`