Question

let s denote the length of the arc of a circle of radius r subtended by the central angle θ. find the missing quantity.
θ = 1/5 radian, s = 6 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 of the circle, and $\theta$ is the central angle in radians.

Step2: Solve for $r$

Given $s = 6$ feet and $\theta=\frac{1}{5}$ radian. Rearranging the formula $s = r\theta$ for $r$, we get $r=\frac{s}{\theta}$.

Step3: Substitute values

Substitute $s = 6$ and $\theta=\frac{1}{5}$ into the formula $r=\frac{s}{\theta}$. So $r=\frac{6}{\frac{1}{5}}$.

Step4: Calculate $r$

Using the rule of dividing by a fraction ($a\div\frac{b}{c}=a\times\frac{c}{b}$), we have $r = 6\times5=30$ feet.

Answer:

30