How to Find the Radius of an Angle

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How to Find the Radius of an Angle
A compass, used to accurately draw circular objects, is adjusted by changing the length of the radius. (compass image by Sid Viswakumar from Fotolia.com)

The radius of an angle is defined as the line segment that begins at the centre of the circle upon which the arc of the angle falls and terminates on the perimeter of the circle. Any given arc length will fall between two radii of the same circle, suggesting that the values of the angle and the arc length subtended by the angle determine the length of the radius. Thus, the geometric relationship between the angle, the arc length and the radius allows for the calculation of this quantity.

Skill level:
Easy

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Things you need

  • Protractor
  • Ruler

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Instructions

  1. 1

    Write down the value of the angle for which you are calculating the radius. This value shall be represented by the variable A.

  2. 2

    Determine the arc length subtended by the angle and label this value as S. If this is not so easily found, measure the line segment between the two radii that act as boundaries for the angle--this measurement will run from one point on the perimeter of the circle to a second point on the same perimeter--denote this quantity as L.

  3. 3

    Write down the appropriate relationship between the quantities determined. If the arc-length is known, write the relationship as r = S/A, where r is the radius. If the line segment that connects the two perimeter points that define the angle is known, write the relationship as r = L/(sin(A) where "sin" is the trigonometric sine function.

  4. 4

    Enter the appropriate relationship into your calculator to get the value of the radius.

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