Question

1. find the length of the bolded arc. round to the nearest hundredth.

arc length = ft

1. if ps = 28 feet, use the circle below to find the length of rpt. round to the nearest hundredth.

length of rpt = ft

Explanation:

Step1: Recall the arc - length formula

The formula for the arc length \(s\) of a circle is \(s=\frac{\theta}{360}\times2\pi r\), where \(\theta\) is the central angle in degrees and \(r\) is the radius of the circle.

Step2: Solve for problem 10

Given \(r = 14.5\) ft and \(\theta=73^{\circ}\).
Substitute into the formula:

$$
LATEXBLOCK0
$$

$$s=\frac{2117\pi}{360}\approx\frac{2117\times3.14159}{360}\approx18.51$$

Step3: Solve for problem 11

First, find the central angle of \(\overset{\frown}{RPT}\).
The sum of angles around a point is \(360^{\circ}\). Given \(PS\) is a diameter (\(180^{\circ}\)), but we can also calculate \(\theta = 360-(97 + 125)=138^{\circ}\) (by subtracting the non - relevant angles from \(360^{\circ}\)). The radius \(r=\frac{PS}{2}=\frac{28}{2} = 14\) ft.
Substitute into the arc - length formula \(s=\frac{\theta}{360}\times2\pi r\):

$$
LATEXBLOCK1
$$

$$s=\frac{3864\times3.14159}{360}\approx33.89$$

Answer:

1. \(18.51\) ft
2. \(33.89\) ft