1. 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.

1. Show that .
2. 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?
3. At what rate is the distance changing when ?