Question

find the measure of \\( \theta \\), in radians, if \\( r = 5 \\) and the arc length is 15.5. \\( \theta = ? \\) radians

Explanation:

Step1: Recall arc length formula

The formula for arc length \( s \) in radians is \( s = r\theta \), where \( r \) is the radius and \( \theta \) is the central angle in radians.

Step2: Solve for \( \theta \)

We know \( s = 15.5 \) and \( r = 5 \). Rearranging the formula \( s = r\theta \) to solve for \( \theta \), we get \( \theta=\frac{s}{r} \). Substituting the given values, \( \theta = \frac{15.5}{5} \).

Step3: Calculate the value

\( \frac{15.5}{5}=3.1 \)

Answer:

\( 3.1 \)