I have a Zone 6" so the height will be just about the same.
The height will have several factors to consider, namely being the tire size and amount of air. For every 2" of tire will be about 1" of height gain.
I have 35" tires with about 40lbs. The height of my truck is almost right at 7 ft plus about 3 inches for the antenna fin.
So to answer your question, my personal setup would need over 7'3" to clear with no one in the truck.
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