dshalghar
Answered

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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

Sagot :

elcharly64

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

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