a 15 ft ladder leans against wall

Question

a 15ft-long ladder leans on a wall. the bottom of the ladder is 9ft from the wall. if the bottom is pulled 4 ft farther from the wall, how far does the top of the ladder move down the wall? 

Answer 1

sqrt(15^2 - 9^2) = sqrt( 225 - 81) = sqrt( 144) = 12

So at first, the top of the ladder is 12 feet off the ground.

 

THEN  sqrt(15^2 - 13^2) = sqrt( 225 - 169) =sqrt(56)

    = sqrt(4 * 14) = 2*sqrt(14)

So when the ladder is pulled 4 feet farther from the wall,

the base of the ladder is 13 feet away.

The top of the ladder is then 2*sqrt(14) = 7.48331477354788..

 

The top of the ladder moves down 4.516685226452117.....