Question

find the radian measure of the central angle of a circle of radius ( r = 5 ) meters that intercepts an arc of length ( s = 1200 ) centimeters.

the radian measure of the central angle is
(type an integer or a simplified fraction.)

Explanation:

Step1: Convert units to be consistent

First, convert the radius from meters to centimeters. Since 1 meter = 100 centimeters, \( r = 5 \) meters \( = 5\times100 = 500 \) centimeters.

Step2: Use the arc length formula \( s = r\theta \) (where \( \theta \) is in radians)

We know \( s = 1200 \) cm and \( r = 500 \) cm. Rearranging the formula for \( \theta \), we get \( \theta=\frac{s}{r} \).
Substitute \( s = 1200 \) and \( r = 500 \) into the formula: \( \theta=\frac{1200}{500} \).
Simplify the fraction: \( \frac{1200}{500}=\frac{12}{5} \).

Answer:

\(\frac{12}{5}\)