Question

find the length to three significant digits of the arc intercepted by a central angle θ in a circle of radius r. r = 8.48 ft, θ = \frac{\pi}{9} radians the length of the intercepted arc is approximately ft. (round to two decimal places as needed.)

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc $s$ of a circle is $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the central angle in radians.

Step2: Substitute given values

Given $r = 8.48$ ft and $\theta=\frac{\pi}{9}$ radians. Substitute these values into the formula: $s=8.48\times\frac{\pi}{9}$.

Step3: Calculate the value

First, calculate $8.48\times\frac{\pi}{9}=\frac{8.48\pi}{9}$. Since $\pi\approx3.14159$, then $\frac{8.48\times3.14159}{9}=\frac{26.6407832}{9}\approx2.96$.

Answer:

$2.96$