Question

watch the video and then solve the problem given below. click here to watch the video. find the radian measure of the central angle of a circle of radius r = 50 inches that intercepts an arc of length s = 80 inches. the radian measure of the central angle is . (type an integer or a simplified fraction.)

Explanation:

Step1: Recall 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 of the circle, and $\theta$ is the central angle in radians.

Step2: Solve for $\theta$

We need to find $\theta$. Rearranging the formula $s = r\theta$ for $\theta$, we get $\theta=\frac{s}{r}$.

Step3: Substitute given values

Given $r = 50$ inches and $s = 80$ inches. Substitute these values into the formula: $\theta=\frac{80}{50}$.

Step4: Simplify the fraction

$\theta=\frac{8}{5}$ radians.

Answer:

$\frac{8}{5}$