25 foot ladder placed against building. Bottom of ladder is 7 feet from building. If top ladder slips 4 feet how much will bottom slip?

Question

A 25 foot ladder is placed against a building. The bottom of the ladder is 7 feet from the building. If the top the ladder slips 4 feet, how many feet will the bottom slip?

Answer 1

imagine the 2 situations, in side view.  initially, it's a 7-24-25 right triangle; ladder meets wall at 24 ft level.

 

after slippage, base of triangle is 11 and hypotenuse (ladder) is still 25 ft long, so we solve for the other leg = square root of 625 - 121 = 22.45.

 

Therefore the top of ladder slipped down 24 - 22.45 ft = 1.55 ft.