Hoop height calculator?

[NatJ]

She is thinking of having the coop half under the hoop coop, and the rest sticking out....
I figure if the hoop coop is 7 - 8 feet wide, it will be between 5 and 6 feet and change at the apex. The devil is in the detail, however, at five feet above the ground what the width of the coop will be.

OK, that makes sense. You want to know how big of a thing can go inside the hoop, not what fits next to it.

Setting up a panel in place and experimenting with the dimensions may be the quickest way for us to figure it out....
My math skills, such as they once were, are now totally non-existent.

Yes, sometimes it is faster to try something than to figure out what it "should" be. (Especially if there is a way to try it quickly, like bending a panel and measuring, rather than doing a full build to see how it goes.)

Another thing about cattle panels: it is easy for the arch to be a little wider/shorter or narrower/taller than the image says. So if you build the coop first and then bend the panel over it, the panel may curve in a way that fits over the coop, if the coop is anything close to the "right" size.

We don't have supplies on hand, but we're going to check out a neighbor's hoop coop to measure. One of our neighbors is a math prof, so maybe he could decode this mystery.

That also sounds like a good idea.