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MA_775_DIABLO [31]
3 years ago
6

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
Mathematics
1 answer:
ahrayia [7]3 years ago
6 0

Answer:

\displaystyle \theta=0.413\ rad

<em>L= 9.086 feet</em>

Step-by-step explanation:

<u>Area of a Circular Sector</u>

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

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