Question

circle l is shown, where m∠klm = 120°. the circumference of circle l is 18π units. what is the length, in units, of (widehat{km})? round your answer to the nearest tenth.

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(s\) is \(s=\frac{\theta}{360}\times C\), where \(\theta\) is the central angle and \(C\) is the circumference of the circle.

Step2: Identify the values of \(\theta\) and \(C\)

Given that \(\theta = 120^{\circ}\) and \(C = 18\pi\) units.

Step3: Substitute the values into the formula

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Step4: Calculate the numerical value

Since \(\pi\approx3.14\), then \(s = 6\times3.14=18.84\approx18.8\)

Answer:

\(18.8\)