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

Step2: Substitute values

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

Step3: Simplify the expression

Simplify \( 24\times\frac{5\pi}{6} \). \( 24\div6 = 4 \), then \( 4\times5\pi = 20\pi \).

Answer:

20π in