# Solving an equation: finding the arc length

1. Jun 3, 2013

### rockwusho

hello every body ..
According to the picture:

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

2. Jun 3, 2013

### CompuChip

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!

3. Jun 3, 2013

### tiny-tim

welcome to pf!

hello rockwusho! welcome to pf!

alternatively, whenever you see a tangent at a point, always draw the line from that point to the centre of the circle, because … ?

4. Jun 4, 2013

### rockwusho

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....

5. Jun 4, 2013

### tiny-tim

rockwusho, the problem is very clear

use either Compuchip's method or mine …

show us what you get​

6. Jun 4, 2013

### rockwusho

Sorry, I don't know what compuchips method is. What do you mean by that?

7. Jun 6, 2013

### rockwusho

I still waiting for your descriptions ...

8. Jun 6, 2013

### Fredrik

Staff Emeritus
CompuChip is the guy who wrote the first reply you got in this thread.

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.