Question

What is the measure of the central angle of a circle with radius 18 centimeters that intercepts a 12pi centimeters arc?

Answer 1

Explanation:

We'll use s = rt where s is arc length, r is the radius, and t is the angle in radians. After we find the angle in radians, we'll convert it to degrees to get the central angle.

`12\pi=18t` so

`t=(2\pi)/(3)`

That's the arc length in radians. Radians does not measure the central angle so we convert using the fact that pi is the same as 180 degrees:

`(2\pi)/(3)*(180)/(\pi)`

The pi's cancel out and 3 goes into 180 60 times, and 60 times 2 is 120, so the angle measure in degrees is 120