Question

A farmer uses an irrigation sprinkler system that pivots about the center of a circular field. Determine the length of the sprinkler if an area of 2060 square feet is watered after a pivot of 40 degrees? The length of the sprinkler is approximately____

Round two decimal places as needed

Answer 1

Here the irrigation sprinkler is pivoted at an angle `theta=40^@=(40pi)/180` rad.

It waters a circular sector of area `A=2060ft^2`.

If the length of the sprinkler be `L` ft. It will be radius of the circular sector watered.

Hence

`1/2xxtheta" in radian"xxL^2=A`

`=>L=sqrt((2A)/theta)=sqrt((2*2060*180)/(40pi))~~76.8`ft