Question

circle p, diameter qs measures 20 centimeters. what is the approximate length of arc qr? round to the nearest tenth of a centimeter. 9.9 centimeters 19.9 centimeters 21.5 centimeters 43.0 centimeters

Explanation:

Step1: Find the radius

The diameter \(QS = 20\) cm, so the radius \(r=\frac{QS}{2}=\frac{20}{2} = 10\) cm.

Step2: Find the central angle for arc \(QR\)

The central angle \(\theta\) for arc \(QR\): Since \(\angle RPS=123^{\circ}\), then \(\angle QPR = 180^{\circ}- 123^{\circ}=57^{\circ}\)

Step3: Use the arc - length formula

The formula for the length of an arc is \(L=\frac{\theta}{360}\times2\pi r\). Substitute \(\theta = 57^{\circ}\) and \(r = 10\) cm.

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Answer:

9.9 centimeters