Question

consider circle c below, where the central angle is measured in radians. what is the length of the radius? units

Explanation:

Step1: Recall the arc - length formula

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

Step2: Substitute the given values into the formula

We know that \(s = 10\pi\) and \(\theta=\frac{5\pi}{6}\). Substituting into \(s = r\theta\) gives \(10\pi=r\times\frac{5\pi}{6}\).

Step3: Solve for \(r\)

Multiply both sides of the equation \(10\pi=r\times\frac{5\pi}{6}\) by \(\frac{6}{5\pi}\).

$$
LATEXBLOCK0
$$

Answer:

\(12\)