I'm honestly still a little confused by what you're asking, because I don't really see why the relationship between the length/height would be relevant.

There are three aspects of the lid that we need to determine, once it has been rotated in space:

• Its depth - so the distance from the front of the lid to the back of the lid. This is the edge we're rotating in the first place, so we maintain that distance by drawing an ellipse that represents a circle in 3D space, with the axis defined by the hinges serving as the ellipse's minor axis.

• Its height. I eyeballed this in the video demo for the challenge, but to be more precise, you'd just repeat the step for the depth, but for the top-side edge (where for the depth we used the bottom-side edge). If your lid isn't a simple box (and therefore might not have a top-side edge), you'd just end up using a box to figure out the correct rotation, then build whatever fancy lid inside of it.

• Its length - so the distance from one side to the other. This is achieved by simply repeating the same process on the other side. You'll see in the demo video that while I eyeballed the height (instead of adding two ellipses on either side), I did place an ellipse on both sides.

So, in essence, all three dimensions of the rotated lid can be determined by applying the same ellipse/circle based approach, and none of this has anything to do with the chest's height. The only dimension of the chest that actually matters here is the depth, since the depth is what becomes the radius of each of these circles in 3D space.