Question

the radius of a circle is 12 miles. what is the angle measure of an arc bounding a sector with area 10π square miles? give the exact answer in simplest form.

Explanation:

Step1: Usar fórmula del área del sector

$10\pi = \frac{\theta}{360} \times \pi r^2$

Step2: Sustituir r=12

$10\pi = \frac{\theta}{360} \times \pi \times 12^2$

Step3: Simplificar $12^2=144$

$10\pi = \frac{\theta}{360} \times 144\pi$

Step4: Eliminar $\pi$ y simplificar

$10 = \frac{144\theta}{360} \Rightarrow 10 = \frac{2\theta}{5}$

Step5: Resolver para $\theta$

$\theta = 10 \times \frac{5}{2} = 25$

Answer:

25