An acute angle made by side of parallelogram With other pair of parallel sides is 30 degrees.

Question

An acute angle made by a side of a parallelogram With other pair of parallel sides is 30 degrees. If the distance between these parallel sides is 10 cm , find the length of the other side

Answer 1

There's a 30-60-90 triangle here! The distance between horizontal parallel lines is 10 cm, that's the height of the triangle. Its hypotenuse is twice the shorter leg, i.e. one side of the parallelogram is 20 cm.  This involves the two parallel lines, and one transversal with 'corresponding' angles 30^o; so one side of the parallelogram measures 20 cm.

 

But the other transversal's position is not determined and so the length of the other (horizontal) side of the parallelogram cannot be found.

Answer 2

  Assuming that this is what you meant

 

 

    -----------a--b

   /     10->? l  /

  /                l /

 --------------c

 

If angle abc is 30 degrees and you mean that the distance between a and c is 10 then the length of side bc can be obtained by

 

sin(30)=10/x       where x is the length of bc

x= 10/sin(30) = 20