Angle and Altitude of sunlight

[G the G]

Hello All...First off, I am an old guy...it has been 50 years since I was in school and haven't done much math since then beyond calculating the amount of wood that I need for a project for my wife.

I am trying to figure out the altitude of sunlight passing through the atmosphere when the sun dips below the horizon. Specifically, if the sun is 6 degrees below the horizon, obviously, there is no sunlight hitting the surface, but sunlight would be passing through the atmosphere above. At what altitude would one be able to see the sun if it were 6 degrees below the horizon from the point of view of a person on the ground. The earth is roughly 6400Km in diameter.

Thanks for any help you guys can offer.

 

[Dr.Peterson]

I think you're asking, in effect, how high a tower you would have to be on if the horizon is at a 6° angle of depression (that is, looking down from the horizontal to the sun).

If you draw a right triangle with its hypotenuse R+h (earth radius plus your altitude), and its right angle at the horizon (so one leg is R), then we find that cos(6°) = (R+h)/R, and solving this yields y = R(1/cos(6°) - 1) = 6400(1/0.9945 - 1) = 35 km.

 

[G the G]

Thank you...your help is appreciated.