An Earth-observing satellite can see only a portion of the Earth's surface. The satellite has horizon sensors that can direct the angle shown in the...

An Earth-observing satellite can see only a portion of the Earth's surface. The satellite has horizon sensors that can direct the angle  shown in the accompanying figure. Let  be the radius of the Earth (assumed spherical) and  the distance of the satellite from the Earth's surface.

a.    Show that .

b.    Using  find the average rate of change of the distance from the satellite to the surface of the Earth, when  changes from  to  What are the units?

c.    At what rate is the distance  changing when