Question

ps = 28 feet

1. what is the arc length of \\( \overgroup{st} \\) rounded to the nearest hundredth?

Explanation:

Step1: Find the radius of the circle

Since \(PS = 28\) feet and \(PS\) is the diameter of the circle, the radius \(r=\frac{PS}{2}=\frac{28}{2} = 14\) feet.

Step2: Use the arc - length formula

The arc - length formula is \(L=\frac{n\pi r}{180}\), where \(n\) is the central angle and \(r\) is the radius.
The central angle for arc \(\overset{\frown}{ST}\): \(n = 180^{\circ}- 125^{\circ}=55^{\circ}\), and \(r = 14\) feet.
Substitute \(n = 55\) and \(r = 14\) into the formula: \(L=\frac{55\times\pi\times14}{180}\).
First, calculate \(55\times14=770\). Then \(L=\frac{770\pi}{180}\approx\frac{770\times3.14}{180}\).
\(770\times3.14 = 2417.8\), and \(\frac{2417.8}{180}\approx13.43\).

Answer:

\(13.43\) feet