Question

The sides of a parallelogram are 20 feet and 40 feet long, and the smaller angle has a measure of 60°. Find the length of the longer diagonal to the nearest whole number.

Answer 1

Length of the longer diagonal is 53 feet.

Explanation:

We are given that,

Dimensions of the parallelogram is 40 feet and 20 feet and the smaller angle is 60°.

Let, the length of the diagonal be 'x' feet.

As the smaller angle is 60°, then the larger angle will be
`(360-2(60))/(2)` =
`(360-120)/(2)` =
`(240)/(2)` = 120°

Using the Law of Cosines for the triangle made by the diagonal, we have,

`x^(2)=20^(2)+40^(2)-2* 20* 40* \cos120`

i.e.
`x^(2)=400+1600-1600* (-0.5)`

i.e.
`x^(2)=2000+800`

i.e.
`x^(2)=2800`

i.e. x= 53 feet

Thus, the length of the longer diagonal is 53 feet.