What is the formula to solve this problem.
Say I have a tower 100km tall and I want to determine the distance from the base of the tower to where a cable is attached to the ground. The cable forms a $30^\circ$ angle with the tower and starts at the top of the tower. We do not know the length of the cable.
This isn't a simple right angle problem because the altitude is great enough that the earth's radius must be factored in.
All we really know is the top of the tower is 100 km high, the angle between the cable and the tower is $30^\circ$, and the earth's radius is 6371km (lets assume a perfect circle).