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.
-$\mathrm { r } = 18$ feet, $\mathrm { A } = 84$ square feet, $\theta =$ ?
A) $14.86 ^ { \circ }$
B) $1,560,152.87 ^ { \circ }$
C) $29.72 ^ { \circ }$
D) $780,076.43 ^ { \circ }$

Question

Quizplus · Accepted Answer

The formula for the area of a sector is $ A = \frac{1}{2} r^2 \theta $ (where $\theta$ is in radians). Solving for $\theta$, we get $\theta = \frac{2A}{r^2}$. Substituting the given values, $\theta = \frac{2 \times 84}{18^2} = \frac{168}{324} \approx 0.5185$ radians. Converting to degrees, $\theta \approx 0.5185 \times \frac{180}{\pi} \approx 29.72^\circ$.

If a Denotes the Area of the Sector of a Circle