12. if ps = 28 feet, use the circle below to find the length of $ \overparen{r p t} $. round to the nearest hundredth. length of $ \overparen{r p t}=$ ft

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Accepted Answer

# Explanation:
## Step1: Find the radius of the circle
Since $PS = 28$ feet is the diameter of the circle, the radius $r=\frac{PS}{2}=\frac{28}{2} = 14$ feet.
## Step2: Find the central angle of arc $RPT$
The sum of angles in a circle is $360^{\circ}$. The central angle of arc $RPT$, $\theta=360^{\circ}-97^{\circ}=263^{\circ}$
## Step3: Use the arc - length formula
The formula for the length of an arc is $L=\frac{\theta}{360}\times2\pi r$. Substitute $\theta = 263^{\circ}$ and $r = 14$ into the formula:
$$
\begin{align*}
L&=\frac{263}{360}\times2\pi\times14\
&=\frac{263\times28\pi}{360}\
&=\frac{7364\pi}{360}\
&\approx\frac{7364\times3.14}{360}\
&=\frac{23122.96}{360}\
&\approx64.23
\end{align*}
$$

# Answer:
$64.23$

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Question

Explanation:

Step1: Find the radius of the circle

Step2: Find the central angle of arc \(RPT\)

Step3: Use the arc - length formula

Answer: