If you run the calculation the other way around, every satellite has to service a ground patch with about 380 miles radius. And your antenna has to swivel to a point that might be more than 60 degrees away from zenith. So every obstruction of more than 30 degrees above the horizon will lead to at least intermittent disconnects.
I am genuinely curious how you arrived at that number, FWIW – I don't know how to go about calculating something like that.