Question

find the length of an arc intercepted by a central angle 0 in a circle of radius r.
r = 33.02 ft, 0 = \frac{\pi}{36} radians

a. 5.8 ft
b. 8.6 ft
c. 1.4 ft
d. 2.9 ft

Explanation:

Step1: Recall the arc - length formula

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

Step2: Substitute the given values into the formula

Given \(r = 33.02\) ft and \(\theta=\frac{\pi}{36}\) radians. Then \(s=33.02\times\frac{\pi}{36}\).
Since \(\pi\approx3.14\), we have \(s = 33.02\times\frac{3.14}{36}\).
First, calculate \(33.02\times3.14 = 103.6828\).
Then \(s=\frac{103.6828}{36}\approx2.9\) ft.

Answer:

D. \(2.9\) ft