Question

Two opposite sides of a parallelogram each have a length of `35`. If one corner of the parallelogram has an angle of `(5 pi)/12` and the parallelogram's area is `210`, how long are the other two sides?

Answer 1

The other two sides are of `6.21(2dp)` length each.

Explanation:

Let ABCD be the parallelogram of which opposite sides `AB = CD = 35` and corner angle `/_A=5*180/12=75^0` Area of the parallelogram `=AB*h :. 210 = 35*h or h=210/35=6`(h is the altitude i.e DE on AB) Now in the right angled triangle DAE `sin 75=6/(AD) or AD=6/sin75=6.21=BC`[Ans]