how to find side lengths of a parallelogram

Question

A parallelogram has sides of lengths 5 and 9, and one angle is 31°.

 

What is the length of the smaller diagonal?

 

What is the length of the longer diagonal?

 

 

your answer should be accurate to 3 decimal places.

Answer 1

Make a sketch & draw the shorter diagonal; it will be across from 31 degree angle; the sides adjacent to this angle are length 5 & 9.  With those 2 sides & the diagonal, you have a triangle, and you can use the Law of Cosines to find its length.

 

By drawing the parallelogram with its longer diagonal, a triangle is formed having two sides (5 & 9) & said long diagonal, across from 180-31 degree angle.  Law of Cosines again!.