Question

find the radian measure of the central angle of a circle of radius r = 5 meters that intercepts an arc of length s = 1300 centimeters.
the radian measure of the central angle is
(type an integer or a simplified fraction.)

Explanation:

Step1: Convert radius to centimeters

Since 1 meter = 100 centimeters, for $r = 5$ meters, then $r=5\times100 = 500$ centimeters.

Step2: Use the arc - length formula

The formula for the arc - length of a circle is $s = r\theta$, where $s$ is the arc - length, $r$ is the radius and $\theta$ is the central angle in radians. We need to solve for $\theta$. Rearranging the formula gives $\theta=\frac{s}{r}$.
Substitute $s = 1300$ centimeters and $r = 500$ centimeters into the formula: $\theta=\frac{1300}{500}$.

Step3: Simplify the fraction

$\frac{1300}{500}=\frac{13}{5}$.

Answer:

$\frac{13}{5}$