Solve the problem.
-As part of an experiment to test different liquid fertilizers, a sprinkler has to be set to cover an area of 120 square yards in the shape of a sector of a circle of radius 30 yards. Through what angle should the sprinkler be
Set to rotate? If necessary, round the answer to two decimal places.
A) 48°
B) 7.64°
C) 15.28°
D) 11.46°

Question

Quizplus · Accepted Answer

The area of a sector of a circle is given by the formula $ \frac{\theta}{360} \times \pi r^2 $, where $ \theta $ is the angle in degrees, $ r $ is the radius of the circle, and $ \pi $ is Pi. Given that the area of the sector is 120 square yards and the radius is 30 yards, we can set up the equation $ \frac{\theta}{360} \times \pi \times 30^2 = 120 $. Solving for $ \theta $, we find that $ \theta = \frac{120 \times 360}{\pi \times 30^2} $, which simplifies to $ \theta = 15.28 $ degrees when rounded to two decimal places.

Solve the Problem. -As Part of an Experiment to Test Different Liquid Fertilizers