Question

in circle r, rs = 3 and m∠srt = 110°. find the length of st. 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 \(l\) of a circle with radius \(r\) and central angle \(\theta\) (in degrees) is \(l=\frac{\theta}{360}\times2\pi r\).

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

Given that \(r = RS=3\) and \(\theta=m\angle SRT = 110^{\circ}\).

Step3: Substitute the values into the formula

Substitute \(r = 3\) and \(\theta=110\) into \(l=\frac{\theta}{360}\times2\pi r\).

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Answer:

\(\frac{11\pi}{6}\)