Question

the radius of a circle is 12 meters. what is the angle measure of an arc bounding a sector with area 35π square meters? give the exact answer in simplest form.

Explanation:

Step1: Usar fórmula del área del sector

$K = \frac{\theta}{360^\circ} \cdot \pi r^2$

Step2: Sustituir valores conocidos

$35\pi = \frac{\theta}{360^\circ} \cdot \pi (12)^2$

Step3: Simplificar y despejar θ

$35 = \frac{\theta \cdot 144}{360^\circ} \implies \theta = \frac{35 \cdot 360^\circ}{144} = \frac{175^\circ}{2}$

Answer:

$\frac{175}{2}$