Question

find the length of arc abc. use 3.14 for the value of π. round to the nearest hundredth of a cm.

Explanation:

Step1: Recall the arc - length formula

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

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

From the problem, \(\theta = 120^{\circ}\) and \(r = 17\space cm\), and \(\pi=3.14\).

Step3: Substitute the values into the formula

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First, calculate \(2\times3.14\times17 = 6.28\times17=106.76\). Then, \(s=\frac{106.76}{3}\).

Step4: Perform the division

\(s=\frac{106.76}{3}\approx35.59\space cm\)

Answer:

\(35.59\space cm\)