An ant is walking around the perimeter of a circular wreath with a radius of 8 inches. 

Question

An ant is walking around the perimeter of a circular wreath with a radius of 8 inches. 

If the ant walked 21 inches, how many radians is the central angle that intercepts the ant’s path?

Answer (Expert Verified)

The movement of the ant illustrates the length of an arc

The measure of the central angle is 2.625 radians

How to determine the central angle

The radius of the arc is given as:

The distance walked is given as:

The length of an arc is

So, we have:

Divide both sides by 8

Divide

Hence, the measure of the central angle is 2.625 radians

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