 One application of this trapezoid result is in the crossed ladders problem, where two ladders lie oppositely across an alley, each with feet at the base of one sidewall, with one leaning against a wall at height "A" and the other leaning against the opposite wall at height "B", as shown.The ladders cross at a height of "h" above the alley floor.Then "h" is half the harmonic mean of "A" and "B".