
Ladder against a box problem
Posted:
Jun 20, 2014 8:13 AM


I was asked to help with a problemsolving night for the local scout troop, and one of the problems was the wellknown (so I now understand) problem of finding the height above ground of a 5m ladder pushed up against a 1m squaresection box against a wall. The scouts were expected to solve this with a scale drawing, which they did, but I had a go a solving it mathematically, which I failed to do in the time available. \  \ \   \ \   \ \   \ \   \ h x  \ \  ______\ \   1 \ \   1 1 \ \  ________\ 1
I've since websearched for solutions, and found some numerical solutions for a 5m ladder, which as an exercise, I tried to convert into a short Python program to give a solution for a ladder of any specified length, but discovered that wasn't so easy because the algebraic solutions that I found seemed to depend on the ladder being of length 5.
Can it be reduced to an equation, or a short sequence of equations?

