Question

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

Explanation:

Step1: Recall arc - length formula

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

Step2: Identify given values

We are given that $s = 10\pi$ and $\theta=\frac{5\pi}{6}$.

Step3: Solve for radius $r$

Substitute the given values into the formula $s = r\theta$: $10\pi=r\times\frac{5\pi}{6}$.
To solve for $r$, we can rewrite the equation as $r=\frac{10\pi}{\frac{5\pi}{6}}$.
When dividing by a fraction, we multiply by its reciprocal, so $r = 10\pi\times\frac{6}{5\pi}$.
The $\pi$ terms cancel out, and $10\times\frac{6}{5}=12$.

Answer:

12