The figures indicate that the higher the orbit of a satellite, the more of the earth the satellite can "see." Let θ, s, and h be as in the figure, and assume the earth is a sphere of radius 3960 miles.
(a) Express the angle θ as a function of h.
θ(h) =
(b) Express the distance s as a function of θ.
s(θ) =
(c) Express the distance s as a function of h. (Find the composition of the functions in parts (a) and (b).)
s(h) =
(d) If the satellite is 120 mi above the earth, what is the distance s that it can see? (Round your answer to the nearest whole number.)
s = mi
(e) How high

Question

The figures indicate that the higher the orbit of a satellite, the more of the earth the satellite can "see." Let θ, s, and h be as in the figure, and assume the earth is a sphere of radius 3960 miles.
(a) Express the angle θ as a function of h.
θ(h) =   
(b) Express the distance s as a function of θ.
s(θ) =   
(c) Express the distance s as a function of h. (Find the composition of the functions in parts (a) and (b).)
s(h) =   
(d) If the satellite is 120 mi above the earth, what is the distance s that it can see? (Round your answer to the nearest whole number.)
s =   mi
(e) How high

anonymous · Answer

$$\theta(h)=\tan^{-1} \frac{ h }{ 3960 }$$ Is what I had, but it was marked wrong.  I need some help with this as I thought I understood which way to go with this, but I was wrong.

anonymous · Answer

$$\theta \left( h \right)=\cos^{-1} \left( \frac{ h }{ 3960 } \right)$$ is this right?

anonymous · Answer

$$\theta(h)=\cos^{-1} (\frac{ 3960 }{ h+3960 })$$