Question

in circle d, de = 7 and m∠edf = 45°. find the length of (overset{\frown}{ef}). express your answer as a fraction times π (in simplest form).

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(s\) is \(s=\frac{\theta}{360}\times2\pi r\), where \(\theta\) is the central angle in degrees and \(r\) is the radius of the circle.

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

Given that \(\theta = m\angle EDF=45^{\circ}\) and \(r = DE = 7\).

Step3: Substitute the values into the formula

Substitute \(\theta = 45\) and \(r = 7\) into \(s=\frac{\theta}{360}\times2\pi r\).

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Answer:

\(\frac{7\pi}{4}\)