Question

consider circle t with radius 24 in. and ( \theta = \frac{5pi}{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 these into the formula: \( s = 24\times\frac{5\pi}{6} \).

Step3: Simplify the expression

Simplify \( 24\times\frac{5\pi}{6} \). First, divide 24 by 6: \( \frac{24}{6}=4 \). Then multiply by 5: \( 4\times5 = 20 \). So \( s = 20\pi \) inches.

Answer:

20π in.