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) $48 ^ { \circ }$
B) $7.64 ^ { \circ }$
C) $15.28 ^ { \circ }$
D) $11.46 ^ { \circ }$

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 and $ r $ is the radius of the circle. 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 (30)^2 = 120 $. Solving for $ \theta $, we find $ \theta = \frac{120 \times 360}{\pi \times 900} $, which simplifies to $ \theta = \frac{120 \times 360}{2827.43} \approx 15.28 ^ { \circ }$.

Solve the Problem 48∘48 ^ { \circ }48∘ B) 7.64∘7.64 ^ { \circ }7.64∘

Solve the Problem $48 ^ { \circ }$ B) $7.64 ^ { \circ }$