A rope hangs from the ceiling. It reaches the floor exactly. It is 4 feet from the wall. When it is pulled to the wall, the end of the rope is 4 inches above the floor. How high is the ceiling?

Answer 1

4" = 1/3 ft

so, reviewing your diagram,

(h - 1/3)^2 + 4^2 = h^2
h = 145/6 = 24'2"