draw a circle to represent the earth.

place a point (the satellite) above the earth's surface. (not very far, consider your scale of miles)

draw two lines tangent to the earth that pass through the point.

from the earth's center, draw lines to the two points of tangency on the earth's surface and one to the satellite point.

two congruent right triangles are formed. using one of them ...

hypotenuse = 4100 miles

long leg = earth's radius = 4000 miles

angle at earth's center =

central angle that intercepts the satellite's transmission arc is double that angle ...

now, remember this equation? ...