# Math Help - Working with Arcs (Radius as function of height?)

1. ## Working with Arcs (Radius as function of height?)

I have an arc of known distance (I don't know what other information is needed for an arc but I can supply it) with two lines of known distance that form a right angle. From this arc I need two things. First I need a function that describes x for any h (where x and h form a right angle). Second I need to draw an arc which for any h has a measure of x + 2/3x. Any suggestions are appreciated.

I have provided an attachment showing the setup I am talking about.

2. ## Re: Working with Arcs (Radius as function of height?)

Why are you mentionning "radius" in "title", but no reference to radius in the problem statement?

With your example (legs 4 and 8), the chord that supports the arc is the hypotenuse,
so 4SQRT(5) = ~8.944 ; agree?

The radius that makes that possible (arc = ~9.342) = ~9.182, and supporting angle = ~58.308 deg.
I believe this can only be obtained by numeric methods; that what I used anyway: ye olde brute force!

I'll wait for your reply: is anything else (such as radius) given?
Do you agree with my radius and angle calculation above?

3. ## Re: Working with Arcs (Radius as function of height?)

Thanks for the reply. I mentioned radius mistakenly because this is actually a simplification of a 3d problem and the x measure translates into the radius of circle (this is the profile of a cone with curved surface). Based on someone's suggestion to simplify the problem I am now using a circular arc l=9.273 r=10 with the segments of 4 and 8 so that (x + 6)^2 + h^2 = 10^2. At this point I need to know if there is an easy way to draw a second arc so that at height h, distance y = x+2/3x .

4. ## Re: Working with Arcs (Radius as function of height?)

Well, all I can contribute is with r=10 and segments = 4 and 8, arc = ~9.273 is correct.
The rest is a "mystery" to me, more so thay you've thrown in a "y"....
Hope someone else can help you.