Question

find the length s of the arc of a circle of radius 30 centimeters subtended by the central angle 30°.
s (arc length) =
centimeters
(type an integer or decimal rounded to three decimal places as needed.)

Explanation:

Step1: Convert the angle to radians

The formula for arc length is \(s = r\theta\), where \(\theta\) must be in radians. We know that \(1^{\circ}=\frac{\pi}{180}\) radians. So for \(\theta = 30^{\circ}\), \(\theta=30\times\frac{\pi}{180}=\frac{\pi}{6}\) radians.

Step2: Calculate the arc length

Given \(r = 30\) centimeters and \(\theta=\frac{\pi}{6}\) radians. Substitute into the arc - length formula \(s=r\theta\). Then \(s = 30\times\frac{\pi}{6}\).

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Answer:

\(15.708\)