The 'height' of the ceiling is eight feet. [=the ceiling is eight feet above the floor; the ceiling is eight feet high]
It was 'the height of' stupidity to quit the team. [=it was extremely stupid to quit the team]
He was 'at the height of' his fame when he died. [=he died when he was most famous]
(..) Ten miles southwest of Metropolis Airport. Notify them the president's on board. present position miles, that's miles southwest of Metropolis Airport. Heading: --, height: feet. What the hell happened? We got our engine back? What the hell's going on out there? Fly, don't look, just fly. (..)1978 Superman