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Math Help - what direction to walk to make slope 26.6 deg

  1. #1
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    what direction to walk to make slope 26.6 deg

    there is a 45 degree hill, z is up, y is north (the hill is sloped towards north), and x is east (hill is parallel to east). What direction should a hiker move so that the slope is 1/2 (i.e. 26.6 degrees)?

    Intuitively I'd say the vector <1,1> because that's in between 45 degrees and zero
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  2. #2
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    Quote Originally Posted by superdude View Post
    there is a 45 degree hill, z is up, y is north (the hill is sloped towards north), and x is east (hill is parallel to east). What direction should a hiker move so that the slope is 1/2 (i.e. 26.6 degrees)?

    Intuitively I'd say the vector <1,1> because that's in between 45 degrees and zero
    If you walked up the hill (from the bottom to the top) you would be a distance above the bottom. Since the hill slopes at a 45 degrees angle you are also that horizontal distance from the bottom. (Its a 1:1 slope)
    Call that vertical & horizontal distance 1.

    If you walk along the top of the hill (parallel with the bottom) for a distance x.
    The HORIZONTAL distance back to the starting point would be \sqrt {1^2 + x^2}.

    You are looking for the horizontal distance, in this case, to be 2.

    You have a triangle. Base (adjacent side) of length 1, and the hypotensue of length 2.

    The angle you require (from the north direction straight up the hill):

     ArcCosine \left( \dfrac{1}{2} \right )
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  3. #3
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    Quote Originally Posted by aidan View Post

    If you walk along the top of the hill (parallel with the bottom) for a distance x.
    The HORIZONTAL distance back to the starting point would be \sqrt {1^2 + x^2}.


    [/tex]
    If I walk x distance along top of hill, is that the same as moving x horizontal distance?

    Wait a minute I think I see what's going on here
    Last edited by superdude; October 1st 2009 at 07:53 PM.
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