Math Circles (Trigonometry) Hard Problem
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Math Circles (Trigonometry) Hard Problem

[From: ] [author: ] [Date: 11-10-17] [Hit: ]
... Assume the earth is a Perfect sphere when answering this question. NOTE: the farther the Satellite is from earth the more earths surface is accessible-Draw the tangent lines from the satellite. How far apart in arc can those tangent points be?......
What is the smallest number of satellites that would be able to broadcast a signal from a single station on earth so that every party of the equator could receive a signal? provide an explanation as well as any necessary diagrams (witch i will do)..... Assume the earth is a Perfect sphere when answering this question. NOTE: the farther the Satellite is from earth the more earths surface is accessible

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Draw the tangent lines from the satellite. How far apart in arc can those tangent points be? Can there be more than 180 degrees between them? Can there be exactly 180 degrees? If so, you could do it with 2 satellites, each covering 180 degrees.

If not, could each cover 120 degrees = 360/3? If so, you could use 3 satellites. You will have to explain how to cover 180 degrees, or 120 degrees, or something smaller by using whatever you know about tangents and the arc length between them.
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