Degree Measure of Central Angle

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Discussion Overview

The discussion revolves around calculating the degree measure of the central angle of a sector in a circle, given the radius and the area of the sector. The context includes mathematical reasoning and application of formulas related to circular geometry.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant proposes using the formula A = (1/2)(r^2)(theta) to find the central angle.
  • Another participant confirms that while using the formula is not mandatory, it is a valid approach and prompts for the calculation of theta in radians first.
  • A participant calculates theta as 40/9, providing both the degree measure (254.6°) and the radian measure (4.444 radians).
  • Subsequent replies affirm the correctness of the calculated values.

Areas of Agreement / Disagreement

Participants generally agree on the correctness of the calculations presented, with no significant disagreements noted.

mathdad
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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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