If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If
necessary, round the answer to two decimal places.
-$r = 9$ feet, $A = 39$ square feet, $\theta =$ ?
A) $0.48$ radians
B) 3,159 radians
C) $0.96$ radians
D) $1,579.5$ radians

Question

Quizplus · Accepted Answer

The area of a sector of a circle is given by the formula $A = \frac{1}{2}r^2\theta$, where $A$ is the area, $r$ is the radius, and $\theta$ is the central angle in radians. Given $A = 39$ square feet and $r = 9$ feet, we can solve for $\theta$ as follows: $39 = \frac{1}{2} \times 9^2 \times \theta$, which simplifies to $39 = \frac{1}{2} \times 81 \times \theta$, and further to $39 = 40.5 \times \theta$. Solving for $\theta$ gives $\theta = \frac{39}{40.5} = 0.96$ radians.

If a Denotes the Area of the Sector of a Circle