Question

consider circle t with radius 24 in. and $\theta = \frac{5\pi}{6}$ radians. what is the length of minor arc sv?
$\bigcirc$ $20\pi$ in.
$\bigcirc$ $28\pi$ in.
$\bigcirc$ $40\pi$ in.
$\bigcirc$ $63\pi$ in.

Explanation:

Step1: Recall arc length formula

The formula for arc length $s$ when the central angle $\theta$ is in radians is $s = r\theta$, where $r$ is the radius of the circle.

Step2: Substitute given values

Substitute $r = 24$ in. and $\theta = \frac{5\pi}{6}$ into the formula:
$s = 24 \times \frac{5\pi}{6}$

Step3: Calculate the product

Simplify the expression:
$s = \frac{24 \times 5\pi}{6} = 4 \times 5\pi = 20\pi$

Answer:

20π in.