Question

find the radius of the circle in which the central angle \\(\alpha = 3\\) intercepts an arc of length \\(s = 15\\) km.\
\\(\\)\
the radius is \\(\square\\) km.\
(simplify your answer.)

Explanation:

Step1: Recall arc length formula

The formula for arc length \( s \) in a circle with central angle \( \alpha \) (in radians) and radius \( r \) is \( s = r\alpha \).

Step2: Solve for radius \( r \)

We know \( s = 15 \) km and \( \alpha = 3 \) radians. Rearranging the formula \( s = r\alpha \) to solve for \( r \), we get \( r=\frac{s}{\alpha} \). Substituting the given values, \( r = \frac{15}{3} \).

Step3: Calculate the value

\( \frac{15}{3}=5 \).

Answer:

5