A ladder 10 ft long leans against a wall. The bottom of the ladder is 6 ft from the wall. How much would the lower end of the ladder have to be pulled away so that the top end would be pulled down by 3 ft?

Answer 1

draw the picture
h is height along the wall
x is the distance along the floor from the wall

x^2+h^2=10^2
36+h^2=100
h= 8

2xdx+2hdh=0
dx=-h/x dh

dh=-3, x=6, h=8, dx= 8*3/6= 4ft
check that.