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Math Help - homework question...pythag th i think

  1. #1
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    homework question...pythag th i think

    Assume the earth is a perfectly round sphere with a radius of 4000 miles and that 1 mile=5280 feet. How far does the horizon appear to be to a 5-ft person on a clear day? Explain.


    i thought the answer would be just a small fraction over 4000 miles, so essentially the height of the man does not change how far the horizon appears to the man.

    am i on the right track here?
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  2. #2
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    Quote Originally Posted by igottaquestion View Post
    Assume the earth is a perfectly round sphere with a radius of 4000 miles and that 1 mile=5280 feet. How far does the horizon appear to be to a 5-ft person on a clear day? Explain.


    i thought the answer would be just a small fraction over 4000 miles, so essentially the height of the man does not change how far the horizon appears to the man.

    am i on the right track here?
    You are dealing with a right triangle. (See attachment)

    The distance from the eye of the observer to the horizon is calculated according to Pythagorean theorem:

    d^2+4000^2 = \left(4000+\frac5{5280}\right)^2

    Solve for d
    Spoiler:
    I've got d \approx 2.75\ mi. If you want to increase the radius of the field of observation you should climb a hill or use a lighthouse.
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