Question

what is the arc length the car traveled, to the nearest hundredth? 2.18 feet 4.31 feet 5.84 feet 6.63 feet

Explanation:

Step1: Find the radius of the circle

Given the diameter \(d = 20\) feet, the radius \(r=\frac{d}{2}\).
\(r=\frac{20}{2}=10\) feet.

Step2: Use the arc - length formula

The arc - length formula is \(s=\frac{\theta}{360}\times2\pi r\), where \(\theta = 38^{\circ}\) and \(r = 10\) feet.
Substitute the values into the formula: \(s=\frac{38}{360}\times2\pi\times10\).
First, simplify \(\frac{38}{360}\times20\pi=\frac{38\pi}{18}\).
Now, calculate \(\frac{38\times3.14}{18}\) (using \(\pi\approx3.14\)).
\(38\times3.14 = 119.32\), then \(\frac{119.32}{18}\approx6.63\).

Answer:

\(6.63\) feet