A 20 feet long ladder that was leaning against the vertical wall and it formed a right triangle with the ground. The top end of the ladder was sliding down at the rate of negative 4 feet per second (because the vertical side of the right triangle was getting shorter and shorter at that same rate). Required:
a. How fast was the bottom end of the ladder skidding away when the bottom end of the ladder was 16 feet away from the wall?
b. At the same moment as above, what was the rate change of the angle of elevation in radians per second (angle formed by the bottom end of the ladder with the ground)?
c. Also, what was the rate change of the area of the right triangle that was formed by the ladder, the wall, and the ground at that same moment?