Question

the radius of a circle is 17 centimeters. what is the measure, in radians, of the angle subtended by an arc 17π centimeters long?
give the exact answer in simplest form.
radians

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(s\) of a circle with radius \(r\) and central angle \(\theta\) (in radians) is \(s = r\theta\).

Step2: Solve for \(\theta\)

We are given that \(s=17\pi\) cm and \(r = 17\) cm. Substitute these values into the formula \(s=r\theta\). Then \(\theta=\frac{s}{r}\).
Substitute \(s = 17\pi\) and \(r = 17\) into \(\theta=\frac{s}{r}\), we get \(\theta=\frac{17\pi}{17}\).
Simplify the fraction \(\frac{17\pi}{17}\), the \(17\) in the numerator and denominator cancels out.

Answer:

\(\pi\)