Solving an equation: finding the arc length

  • Context: High School 
  • Thread starter Thread starter rockwusho
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    Arc Arc length Length
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Discussion Overview

The discussion revolves around finding the equation for the arc length of a circle based on known parameters, specifically the radius and height related to a tangent line. Participants explore the geometric relationships involved in calculating the arc length from these parameters.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant suggests that the tangent and height form a triangle, allowing the calculation of the third side, which is a chord of the circle, from which the arc length can be derived.
  • Another participant emphasizes the importance of drawing a line from the tangent point to the center of the circle for clarity in solving the problem.
  • A participant expresses concern that the problem was not clearly described and reiterates the need to relate the arc length to the height parameter.
  • There is a mention of a method referred to as "CompuChip's method," but its details are not provided, leading to confusion among some participants.
  • Participants indicate that they will provide hints rather than complete solutions, encouraging the original poster to attempt solving the problem with the hints given.

Areas of Agreement / Disagreement

Participants generally agree that the problem involves geometric relationships between the radius, height, and tangent line. However, there is disagreement regarding the clarity of the problem description and the specific methods to be used in solving it.

Contextual Notes

There are limitations in the clarity of the problem description and the specifics of the methods mentioned, which may affect the participants' ability to provide targeted assistance.

rockwusho
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hello every body ..
According to the picture:

03283495774799076533.gif


Circle radius (Radius) and height (High) is known to us. Given that the height of the draw the tangent line , I looking for the equation for length of the arc (Arc Length) was calculated based on height changes.

(sorry for my written objections!)

thanks
 
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The tangent and the height form two sides of a triangle, so you can calculate the third side.
That side is also a chord of the circle, and from a chord length and radius you can calculate arc length.

Give it a try and let me know where you get stuck!

PS If it would be possible for you to scale that image down a bit, that would be great!
 
welcome to pf!

hello rockwusho! welcome to pf! :smile:

alternatively, whenever you see a tangent at a point, always draw the line from that point to the centre of the circle, because … ? :wink:
 
I think the problem was not described clearly. The problem is: the radius of the circle and the parameter High are known.
Given that the line from the top of High is tangent to the circle, we are looking for the equation relating the length of the arc to the parameter high...
 
rockwusho, the problem is very clear

use either Compuchip's method or mine …

show us what you get​
 
Sorry, I don't know what compuchips method is. What do you mean by that?
 
I still waiting for your descriptions ...
 
rockwusho said:
Sorry, I don't know what compuchips method is. What do you mean by that?
CompuChip is the guy who wrote the first reply you got in this thread.

rockwusho said:
I still waiting for your descriptions ...
Everyone else is still waiting for yours. We will only give you hints, not complete solutions. When you've been given a hint or two, you need to try to use them. If you're having problems with this, you need to explain what the problem is.
 

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