A ladder 25 feet long is leaning against
the wall of a house (see figure). The base of the ladder is
pulled away from the wall at a rate of 2 feet per second
(a) How fast is the top of the ladder moving down the wall
when its base is 7 feet, 15 feet, and 24 feet from the wall?
(b) Consider the triangle formed by the side of the house, the
ladder, and the ground. Find the rate at which the area
of the triangle is changing when the base of the ladder is
7 feet from the wall.
© Find the rate at which the angle between the ladder and the
wall of the house is changing when the base of the ladder
is 7 feet from the wall.