The trade is called cooper. The angle would be determined by how many staves the barrel would have. There is 360 degrees in a circle and you would just divide by how many joints. The hard part is the barrel is wider in the middle so the staves have to be wider in the middle and cut on a curve and it has to be made to fit the metal rings. Could take a person quite a while to work out how to precisely cut the parts once you come up with the dimensions. I don't know where a person could buy the hoops either.
There is something on the net called "Behind the Scenes" barrel making at Jack Daniels but it takes better internet than I have.
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