On a 10' rise a 2x12 stringer is good. I would put a post under it in the middle just to take the bounce out. The maximum rise between landings (according to the Building Code of Canada) is 12', but a landing in the middle of a 10' rise would certainly be a good idea. You could change direction as well, if desired.
Put in two stringers for 3' wide treads 1 1/2" thick, with the treads overlapping the stringer 4" to 6". Wider than 3' use more stringers, at about 2' centers.
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