# Ladder around a corner problem

This a problem often encountered in some upper secondary and university level mathematics textbooks. It asks what is the maximum length of a ladder (essentially a line segment) that can be moved around the corner between two corridors. Typically the problem specifies the widths of each corridor and that the angle between the corridors is 90 degrees. All three of these parameters (widths of corridor and angle between corridors) can be changed to present a different problem. Start with the 'simplest' version of the problem where each corridor has a width of one unit and the angle between the corridors is 90 degrees - and find the length of the longest ladder (line segment) that can be moved around the corner.

The GeoGebra applet below is an interactive model for exploring this 'ladder around a corner' problem. When first opened, the applet presents the conditions (given above) for the simplest version of the problem. However, other versions of the problem can be explored by changing the corridor widths and angle between the corridors in the applet. Some further notes and solutions will soon be added to this page. Any comments are welcome and can be submitted at the bottom of the page.