Eight feet at least, ten to fourteen is good, twenty is about the most they usually needed to be. High enough to keep the wires free of livestock and passers-by, keeping in mind sagging wires in summer and drifting snow in winter.
Much depended on who put them in - telegraph poles were normall cut locally, hauled to the site and erected by contract crews. Being picky about the height meant more time looking for good trees, especially in the prarie, plus taller poles required deeper holes which meant more time to dig. Thus paid by the mile meant taking whatever shortcuts one could, so the farther from town the shorter the poles tended to become.
Add to this the fact there was no danger of the lines electrocuting anyone and you find rather short poles.