Bending a triangle? (modeling horn subwoofers)

[SexieWASD]

I'm working on 3d modeling horn subwoofers and have run into a problem that I can't figure out how to solve by myself. I've been learning calculus from khan academy videos in an attempt to solve this, but I feel that it is still out of my reach.

Here is an image to help explain the problem:

There is a triangle (horn) with an arbitrary slope and length. I want to be able to bend the triangle at any point along it's length, to any angle 0 to 180 deg. The length is measured with a line down the center of the triangle. The bend has a arbitrary constant inside radius.

Here is the problem:
The bend needs to have the same slope as the triangle, Width/Length.
Width is measured from the inside radius to the outside at any angle theta with the polar center being the center of the inside radius.
The Length is the arc length of the curve from Width/2 at theta = 0, to Width/2 at any point along the line. any point on the arc is the middle point at that angle.

To figure out the arc length from 0 to point A I need to know the Width at point A, To know the Width at point A I need the arc length from 0 to point A.

 

[SexieWASD]

Though that I would post a little bit more information incase it helps. It may help me just to write it out.
The Angle of the bend, The Slope (expansion rate) of the horn, The Width at the start of the bend, and the inside radius are all known values at the start of the problem.
Angle = θ
Slope = S
Width = W
Inside radius = I

The Width at any Angle θ > 0, and the arc Length at any Angle θ, are not known, but their ratio to each other is known, as it should be the same as if the horn is not bent.
arc Length = L

If we start with a width of 1unit and have an arc Length of 2units the width should be = (W / S + L) * S
if the slope is .132units, 1 / .132 = 7.5757575758, + 2 =
9.5757575758, * .132 gives us a width of 1.264units.

I don't know how to find the Width/Length combination for any Angle θ. If you make the Width larger the midpoint moves too, changing the arc Length with it.