Question

what is the length of the bolded arc?
18 numeric 1 point
a sector has radius 10 m and area \frac{80}{9}\pi m^2. what is the measure, in degrees, of the central angle of the sector?
answer
19 numeric 1 point
what is the arc length of? round to the nearest whole number, if necessary. use \pi = 3.14.
answer

Explanation:

Step1: Recall the formula for arc length

The formula for the arc length \(L\) of a sector with central angle \(\theta\) (in degrees) and radius \(r\) is \(L=\frac{\theta}{360}\times2\pi r\). Here, \(\theta = 150^{\circ}\) and \(r = 19\) ft.

Step2: Substitute the values into the formula

Substitute \(\theta = 150\) and \(r = 19\) into \(L=\frac{\theta}{360}\times2\pi r\). We get \(L=\frac{150}{360}\times2\pi\times19\).
Simplify \(\frac{150}{360}=\frac{5}{12}\), then \(L=\frac{5}{12}\times2\pi\times19=\frac{5\times19}{6}\pi=\frac{95}{6}\pi\approx15.8\pi\)

Answer:

\(15.8\pi\)