Question

consider circle c with angle acb measuring 3π/4 radians. if minor arc ab measures 9π inches, what is the length of the radius of circle c? if necessary, round your answer to the nearest inch.

Explanation:

Step1: Recall the arc - length formula

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

Step2: Substitute the given values into the formula

We are given that \(s = 9\pi\) inches and \(\theta=\frac{3\pi}{4}\) radians. Substituting into \(s = r\theta\), we get \(9\pi=r\times\frac{3\pi}{4}\).

Step3: Solve for \(r\)

To solve for \(r\), we can use the equation \(9\pi=\frac{3\pi r}{4}\). First, multiply both sides of the equation by \(\frac{4}{3\pi}\).

$$
LATEXBLOCK0
$$

Answer:

\(12\) inches