Question about circle arc length formula

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SUMMARY

The formula for the length of an arc that subtends a central angle is correctly expressed as L = (A/360) * C, where L is the arc length, A is the central angle in degrees, and C is the circumference of the circle. This relationship holds true as the arc length is directly proportional to the central angle. Testing the formula with central angles of 360°, 180°, and 90° confirms its validity, reinforcing the intuitive understanding that the arc length increases with the angle.

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shadowboy13
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Now i haven't checked yet whether or not this is correct, but the formula for the length of an arc that subtends a central angle can also be expressed this way: AC/360

Where:
A: Central Angle
C: Circumference

Is this correct?

Thank you for your help.
 
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shadowboy13 said:
Now i haven't checked yet whether or not this is correct, but the formula for the length of an arc that subtends a central angle can also be expressed this way: AC/360

Where:
A: Central Angle
C: Circumference

Is this correct?

Thank you for your help.

Well you tell me. Does the formula match up with what you'd expect if the central angle A = 360o? 180o? 90o? If it doesn't work for one of these values, then it can't be correct, but if it does work for all, then it's pretty good evidence that it could be correct if you also couple it with some simple logic. In other words, is this what you'd expect the arc length to be intuitively?
 
Essentially what you are trying to say is that the length of a segment of a circle of given radius is proportional to the central angle. Yes, that's true.
 

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