536 Puzzles: #309: A Maypole Puzzle

During a gale a maypole was broken in such a manner that it struck the level ground at a distance of twenty feet from the base of the pole, where it entered the earth. It was repaired, and broken by the wind a second time at a point five feet lower down, and struck the ground at a distance of thirty feet from the base. What was the original height of the pole? In neither case did the broken part become actually detached.

From this you can set up the following equations:

(h-x)^2 - x^2 = 30^2

(h-(x+5))^2 - (x+5)^2 = 20^2

Expanding:

h^2 - 2hx  = 30^2

h^2 - 2h(x+5) = 20^2

Subtracting the second from the first yields:

2h*5 = 30^2 - 20^2

h =50  

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