How high should you climb up the tower?

This week’s Riddler classic is a neat geometry problem.

Two people climb two of the tallest towers on an planet, which happen to be in neighboring cities. You both travel 100 meters up each tower on a clear day. Due to the curvature of the planet, they can barely make each other out. The first person returns to the ground floor of their tower. How high up their tower must the second person be you can barely make each other out again?

My solution:
[Show Solution]

2 thoughts on “How high should you climb up the tower?”

  1. I believe that at the vertical asymptote, the towers are 90 degrees apart, not on opposite sides of the planet. The line of sight of the person at the bottom of the tower is parallel to the other tower.

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