Chapter 5.4, Problem 44E

View from a Satellite The figures on the next page indicate that the higher the orbit of satellite, the more of the earth the satellite can “see.” Let $\theta , s,$ and $h$ be as in the figure, and assume that the earth is a sphere of radius 3960 mi.

(a) Express the angle $\theta$ as a function of $h$.

(b) Express the distance $s$ as a function of $\theta$.

(c) Express the distance $s$ as a function of $h$. [Hint: Find the composition of the functions in parts (a) and (b).]

(d) If the satellite is 100 mi above the earth, what is the distance $s$ that it can see?

(e) How high does the satellite have to be to see both Los Angeles and New York, 2450 mi apart?