Question

let s denote the length of the arc of a circle of radius r subtended by the central angle θ. θ = 1/5 radian, s = 5 feet, r =? the radius r of the circle is feet. (simplify your answer.)

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc 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.

Step2: Rearrange the formula to solve for $r$

We can rewrite the formula $s = r\theta$ as $r=\frac{s}{\theta}$.

Step3: Substitute the given values

Given that $\theta=\frac{1}{5}$ radian and $s = 5$ feet. Substitute these values into the formula $r=\frac{s}{\theta}$, we get $r=\frac{5}{\frac{1}{5}}$.

Step4: Simplify the expression

When dividing by a fraction, we multiply by its reciprocal. So $r = 5\times5=25$ feet.

Answer:

25