Question

Two opposite sides of a parallelogram each have a length of `8`. If one corner of the parallelogram has an angle of `(5 pi)/6` and the parallelogram's area is `72`, how long are the other two sides?

Answer 1

Other two sides are `18` unit long.

Explanation:

One parallal sides of parallelogram `s_1=8`
Area of parallelogram `A_p=72`
Angle of one corner is `theta= (5*180)/6=150^0`
We know the area of the parallelogram as `A_p=s_1*s_2*sin theta or 72=8*s_2*sin150 or s_2=72/(8*1/2)=18`Since `sin150=1/2`
Hence other two sides are `18` unit long.[Ans]