Question

company logo
a company has two options for logos as shown. the radius of each logo is 1 foot.

jayson wants to find out specific measurements from each logo.
jayson measures an arc length of a part of one of the logos. let s represent the length of this arc in feet.
which statement describes the radian measure of the central angle that intercepts the arc of length s?
a. the radian measure of the central angle is the ratio of s to 1.
b. the radian measure of the central angle is the ratio of 1 to s.
c. the radian measure of the central angle is the difference of s and 1.
d. the radian measure of the central angle is the difference of 1 and s.

Explanation:

Step1: Recall the formula for radian measure

The formula for the radian measure \(\theta\) of a central angle is \(\theta=\frac{s}{r}\), where \(s\) is the arc - length and \(r\) is the radius of the circle.

Step2: Substitute the given radius

Given that \(r = 1\) foot. Substituting \(r = 1\) into the formula \(\theta=\frac{s}{r}\), we get \(\theta=\frac{s}{1}=s\).

Answer:

A. The radian measure of the central angle is the ratio of \(s\) to \(1\).