Hello, magentarita!

An engineer is asked to design a water sprinkler that will cover a field

of 100 square yards that is in the shape of a sector of a circle of radius 50 yards.

Through what angle should the sprinkler rotate?

We are expected to know the area formula for a sector of a circle: . .[1]

. . where is the radius and is the central angleinradians.

We know: .

Substitute into [1]: .

Therefore: .