How many poles and lines would be needed to create a zipline around the world?

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steadierfooting
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I was trying to figure this out on my own, probably more a trig question then math though. It''s been a few years since I've taken a physics class so forgive me if I'm misusing terminology.

Let's assume I wanted to create a zipline that would take me around the world. You couldn't jus use a x degree angle and use the circumference of the Earth and have one large pole to reach the sky. I'm guessing there would be multiple exsecent lines (poles) where the next pole would be set up where the tangent line reaches the circle (globe). That tangent line probably approaches infinity so I'm looking for approximations, but.

How many 'zip lines' would there need to be disregarding safety, and how long would the total 'lines' be if we were to create a zipline to go around the world?

Thanks for any advice in helping me solve this problem!
 
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