Question

A ladder, 6m long rests against a wall. The foot of the ladder is 2.5m away from the base of the wall. The ladder has a 'safe angle' with the ground between 60(degrees) and 70(degrees). what are the safe limits for the distance of the foot of the ladder to the wall.

Answer 1

If the base of the ladder is at distance b from the wall, and the ladder makes an angle θ with the ground,

b/6 = cosθ

sec 60° = .5
sec 70° = .34

so 6*2 = 3
6*.34 = 2.04

so, the base may safely be between 2 and 3 feet from the wall.