A ladder 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 feet per second.
a. How fast is the top of the ladder moving down the wall when its bases is feet, feet, and 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 feet from the wall.
c. 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 feet from the wall.
