Circumference & Arc Measure: Is this Correct?

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Homework Help Overview

The discussion revolves around the relationship between circumference, arc measures, and angles in a circle, specifically focusing on the calculations involving a circle with a radius of 10. Participants are examining the correctness of the original poster's reasoning and calculations regarding arc lengths and their corresponding angles.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to derive arc measures from given angles and radius, while some participants question the validity of equating degrees to lengths in their calculations. Others seek to clarify the definitions and relationships between circumference and angles.

Discussion Status

The discussion is active, with participants providing feedback on the original poster's calculations and questioning assumptions made in the reasoning. There is no explicit consensus, but some guidance has been offered regarding the correct interpretation of the relationships involved.

Contextual Notes

Participants are navigating potential misunderstandings about the conversion between degrees and arc lengths, as well as the implications of using the circumference formula in this context.

Miike012
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Homework Statement


Just got done reading the chapter... Want to make sure I have this right...

IF Circumference = 2(pi)r
Let cir = 360 deg.
So that 360 deg = 2(pi)r

And 180 deg = (pi)r

IF r = 10
then 180 = (pi)10

Hence half of a cirlce with radius of 10 has an arc measure of 10(pi)...

Is this correct?


And if I wanted to find An arc measure of angle 70 deg I would
solve for x
180x = 70
x = 70/180 = 7/18
then
70 = (7/18)(Pi)(10)
If radius is 10...

Homework Equations





The Attempt at a Solution

 
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360° ≡ 2π

In your working you equated 360 to 2πr meaning that you equated degrees to a length, which is incorrect.
 
isnt the equation for circumference 2(pi)r?
and circumference refers to the entire circle which is 360 deg.
 
Well...
 
Miike012 said:
isnt the equation for circumference 2(pi)r?
and circumference refers to the entire circle which is 360 deg.

360 degrees would be the ratio of the circumference of the circle to its diameter.
 
that's exactly right except that the arc length should be (7pi/18)(10) not (7/18)pi
 

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