for horizontal oil wells the rig head frame is normally kept vertical throughout the well drilling . The bit goes down verticaly untill it gets beneath the shale cap rock where the oil/gas is, and then the drillers are able to manipulate the bit to go horizontal(head frame still vertical) which in theory will increase the potential swept area for oil/gas.
Drilling for minerals the rig itself is inclined from the vertical if needed ie if they are drilling "kimberlite pipe formations " would be a classic example where by drilling vertical it would be difficult to delineate the ore body width between the footwall and hanging wall " thats my understanding, not an oiler or mining engineer though.
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