Question

If the area of a sector is 100 ft^2 and the radius of the circle is 22 ft what is the central angle measure for that sector and what is the length of the arc

Answer 1

Answer:

$\displaystyle \theta=0.413\ rad$

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

$\displaystyle A=\frac{1}{2}r^2\theta$

And the length of the arc is:

$L=\theta r$

We know the area of the sector is 100 square feet and the radius is r=33 ft, thus:

$\displaystyle 100=\frac{1}{2}r^2\theta$

Solving for θ:

$\displaystyle \theta=\frac{200}{r^2}$

$\displaystyle \theta=\frac{200}{22^2}$

$\displaystyle \theta=0.413\ rad$

The arc length is:

$L=0.413* 22$

L= 9.086 feet