Answer :
Answer:
[tex]A\approx 707 \ ft^2[/tex]
Step-by-step explanation:
Area of a circular sector
A circular sector is defined by a central angle θ and the radius of the circle r. The area of the circular sector is:
[tex]{\displaystyle A={\frac {r^{2}\theta }{2}}}[/tex]
Note: θ must be expressed in radians.
The lawn sprinkler rotates θ=90° to an area of radius r=30 feet.
Expressing θ in radians:
[tex]\theta=90*\pi/180=\pi/2[/tex]
The area is:
[tex]{\displaystyle A={\frac {30^{2}\pi/2 }{2}}}[/tex]
[tex]A=706.9\ ft^2[/tex]
[tex]\boxed{A\approx 707 \ ft^2}[/tex]