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Math Help - Height of a mountain

  1. #1
    Junior Member
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    Height of a mountain

    Hi,
    I got bad luck this term and got stuck with an instructor that doesn't even use the book to teach, so I'm really lost on this one problem.

    I have to figure out the height of Mt Kilimanjaro based on two angles of elevation(they are right triangles).

    One angle is 13.7 degrees, and another angle, 10.4 degrees is 5 miles behind the first. Approximate the height of mt kilimanjaro to the nearest 10th of a foot.

    I have this formula so far:

    tan(13.7)=\frac{h}{d}

    dtan(13.7) = h

    d = \frac{h}{tan(13.7)}

    and

    tan(10.4)=\frac{h}{d+5}

    (d+5)tan(10.4) = h

    d+5 = \frac{h}{tan(10.4)}

    d = \frac{h}{tan(10.4)}-5

    After this I'm stuck. h = height of the mountain, or the opposite side, and d = distance from the mountain; adjacent side.

    I have to solve for h.
    If you could explain this to me in a way that doesn't seem esoteric I'd really appreciate it..I have the solution manual with steps but it really doesn't help at all.
    Last edited by qleeq; October 5th 2010 at 11:34 AM.
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  2. #2
    MHF Contributor Unknown008's Avatar
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    You distributed improperly;

    (d+5)tan(10.4) = h

    dtan(10.4) + 5tan(10.4) = h

    This should be okay now
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  3. #3
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    Quote Originally Posted by Unknown008 View Post
    You distributed improperly;

    (d+5)tan(10.4) = h

    dtan(10.4) + 5tan(10.4) = h

    This should be okay now
    oops, what i meant was:
    d = \frac{h}{tan(10.4)}-5
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  4. #4
    MHF Contributor Unknown008's Avatar
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    Right.

    Equate:

    \dfrac{h}{tan(10.4)}-5 = \dfrac{h}{tan(13.7)}

    Multiply by tan(10.4)tan(13.7)

    htan(13.7)-5tan(10.4)tan(13.7) = htan(10.4)

    htan(13.7) - htan(10.4) =5tan(10.4)tan(13.7)

    h(tan(13.7)- tan(10.4)) =5tan(10.4)tan(13.7)

    Finish it now!
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