Question

Suppose that circles R and S have a central angle measuring 60°. Additionally, the length of the intercepted arc for circle R is 10 3 π meters and for circle S is 16 3 π meters.

Answer 1

15.8 meters

Explanation:

We have the following information:

The length of the intercepted arc for the circle R = 103 * π meters

The arc length of circle S = 163 * π meters

We also know the radius of the circle R (10) but not that of the circle S (x).

We are told that circles R and S have a central angle that measures 60 °. Therefore, the radius of circle S to the radius of circle R is equal to the length of the intercepted arc S to the length of the arc R, thus:

Radius S / Radius R = Length S / Length R

I know all, except the radius of S, we organize for this value and we have:

Radius S = (Length S / Length R) * Radius R

Replacing:

Radius S = (163 * π / 103 * π) * 10

Radius S = 15,825 meters

So the radius of the circle S = 15.8 meters