Answer:
[tex]\displaystyle \theta=0.413\ rad[/tex]
L= 9.086 feet
Step-by-step explanation:
Area of a Circular Sector
Given a circle of radius r, the area of a circular sector defined by a central angle θ (in radians) is given by
[tex]\displaystyle A=\frac{1}{2}r^2\theta[/tex]
And the length of the arc is:
[tex]L=\theta r[/tex]
We know the area of the sector is 100 square feet and the radius is r=33 ft, thus:
[tex]\displaystyle 100=\frac{1}{2}r^2\theta[/tex]
Solving for θ:
[tex]\displaystyle \theta=\frac{200}{r^2}[/tex]
[tex]\displaystyle \theta=\frac{200}{22^2}[/tex]
[tex]\displaystyle \theta=0.413\ rad[/tex]
The arc length is:
[tex]L=0.413* 22[/tex]
L= 9.086 feet
