A ladder 16m long is placed so that its foot is 3m away from the building. How far must the foot of the ladder be moved from the building to lower the top of the ladder by 2m?

Answer 1

At the outset the top of the ladder is sqrt(256-9) m above the ground; call that height H

To lower the ladder 2 feet: the distance from the wall will be sqrt[256-(H-2)²].