69. Cable Television Coverage A cable broadcast satellite S orbits a planet at a height h (in miles) above the Earth's surface, as shown in the figure. The two lines from S are tangent to the Earth's surface. The part of the Earth's surface that is in the broadcast area of the satellite is determined by the central angle θ indicated in the figure.
(a) Assuming that the Earth is spherical with a radius of 4000 mi , write h as a function of θ.
(b) Approximate θ for a satellite 200 mi above the surface of the Earth.