Degree Measure of Central Angle

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SUMMARY

The discussion focuses on calculating the degree measure of the central angle for a sector in a circle with a radius of 3 meters and an area of 20 m². The formula used is A = (1/2)(r²)(θ), where A represents the area, r is the radius, and θ is the central angle in radians. The calculated value of θ in radians is 4.444, which converts to 254.6° when expressed in degrees. This demonstrates the application of sector area formulas in geometry.

PREREQUISITES
  • Understanding of circular geometry
  • Familiarity with the formula for the area of a sector
  • Knowledge of converting radians to degrees
  • Basic algebra skills for solving equations
NEXT STEPS
  • Study the derivation of the sector area formula A = (1/2)(r²)(θ)
  • Learn about the relationship between radians and degrees
  • Explore applications of sector area calculations in real-world problems
  • Investigate other geometric shapes and their area formulas
USEFUL FOR

Students studying geometry, educators teaching circular measurements, and anyone interested in mathematical problem-solving involving sectors and angles.

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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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