MHB Degree Measure of Central Angle

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To find the degree measure of the central angle in a circle with a radius of 3 meters and an area of 20 m² for a sector, the formula A = (1/2)(r²)(θ) can be used. Given the area A is 20 and the radius r is 3, the angle θ in radians is calculated to be 4.444. Converting this to degrees, the central angle measures approximately 254.6°. The calculations confirm the accuracy of the results. Understanding these conversions is essential for solving similar geometric problems.
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In a circle of radius 3 meters, the area of a certain sector is 20 m^2. Find the degree measure of the central angle. Round the answer to two decimal places.

Must I use A = (1/2)(r^2)(theta)?
 
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You don't have to but you certainly can!

You are told that A= 20 and r= 3. So what is [math]\theta[/math] in radians (the formula you give requires that [math]\theta[/math] be in radians)? And then what is [math]\theta[/math] in degrees?
 
Theta = 40/9

Theta in degree measure is 254.6°.

Theta in radian measure is 4.444 radians.
 
Yes, that is correct.
 
Very good.
 

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