Question

d = 20 ft
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

Given diameter $d = 20$ ft, radius $r=\frac{d}{2}=\frac{20}{2}=10$ ft.

Step2: Use arc - length formula

The formula for arc - length $s$ of a circle with radius $r$ and central angle $\theta$ (in degrees) is $s=\frac{\theta}{360}\times2\pi r$. Here $\theta = 38^{\circ}$ and $r = 10$ ft. So $s=\frac{38}{360}\times2\pi\times10$.

Step3: Calculate the arc - length

First, simplify the expression:
\[

$$\begin{align*} s&=\frac{38\times2\times10\pi}{360}\\ &=\frac{760\pi}{360}\\ &=\frac{19\pi}{9}\approx\frac{19\times3.14159}{9}\\ &=\frac{59.69021}{9}\approx6.63 \end{align*}$$

\]

Answer:

6.63 feet