There is a 6 metres wide alley. Both walls of the alley are perpendicular to the ground. Two ladders, one 10 metres long, the other 12 metres, are propped up from opposite corners to the adjacent wall, forming an X shape. All four feet of each ladder are firmly touching either the corner or the wall. The two ladders are also touching each other at the intersection of the X shape.

What is the distance from the point of intersection from the ground?

Split the bottom triangle in two using line h.

Using trig, found top angle of left to be 36.87 deg, and top angle of right to be 30.02. Tangent of 36.87 is .75, and tangent of right is .5778.

Since h is part of both triangles, tangent of left added to tangent of right must be 6.0 meters. Having drawn it out, should be around 4.5. Using excel, bumped h up to 4.5187525 to get sum to exactly 6.0.

I notice everyone is using 60 deg for angle in 12 meter ladder, I got 59.98. Just rounding?

Posted by Jim on 2004-10-04 11:11:33