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.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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