Question

The diameter of a circle is 10 miles. what is the angle measure of an arc bounding a sector with area 5​ square miles?

Answer 1

Radius = 5 miles
Sector Area = (central angle / 360) * PI * radius^2
5 = (central angle / 360) * PI * 5^2
(central angle / 360) = 5 / (PI * 5*5)
(central angle / 360) = 1 / (PI * 5)
central angle = 360 / (PI * 5)
central angle = 72 / PI
central angle = 22.9183118052 degrees

Source:
http://www.1728.org/radians.htm