A student made his Frisbee on roof of the common block in Walter Gage Residence. He finds 20-feet-long a ladder which leans against wall in order to climb on the roof. He does not set the ladder well, the bottom of the ladder slides away from the building horizontally at a rate of 3 ft/sec. So how fast is the ladder sliding down the house when the top of the ladder is 16 feet from the ground?

When the ladder leans against wall, the ladder, the wall and the ground between them form a right triangle. According the Pythagorean theorem, square of the height of the wall(h) and square of the length of the ground(l) between the ladder and the wall equals square of the length of the ladder, which is h^2+l^2=20^2. When the top of the ladder is 8 feet from the ground, 16^2+l^2=20^2, so we solved for l, the answer is 12. Then take the derivative of the equation for both sides, 2h*h’+2l*l’=0. As we known, h=16, l=12 and h’=-3 because it slides down, 2*16*(-3)+2*12*l’=0. We can get l’=4 ft/sec.