>>937Not that anon, but
△ABF is a right triangle, so (AB)² + 3² = 5² and AB = 4.
△EFB is a right triangle, so (EF)² + 3² = 4² and EF = √7.
△CDF is similar to △ABF, so DF/BF = CD/AB = h/4.
△CDB is similar to △EFB, so BD/BF = CD/EF = h/√7.
BD and DF together make BF, so DF/BF + BD/BF = h/4 + h/√7 = 1.
Thus h = 1/(1/4 + 1/√7) ≈ 1.5924467752259388 m.