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Math Help - Story Problem

  1. #1
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    Story Problem

    Hi Can you guys help me with this question? I don't remember what to do

    A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 30 degrees. From a point 1500 feet closer to the mountain along the plain, they find that the angle of elevation is 34 degrees

    How high (in feet) is the mountain?
    ___________________
    This is what I know.



    I need to solve for Z so.. I just remeber that you need to solve for x and then z.

    tan 30 = z/1500+x

    tan 43 = z/1500+x

    It's something like that but I do not remember.
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  2. #2
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    Quote Originally Posted by killasnake View Post

    tan 30 = z/1500+x

    tan 43 = z/1500+x

    It's something like that but I do not remember.
    No, your equations are wrong.
    First I thing you mean 34 not 43 but that is not the problem.
    ---
    tan 30=z/(1500+x)

    tan 34=z/x

    From the second equation we
    x tan 34 =z
    Thus,
    x=z/(tan 34)
    Substitute that into first equation,

    tan 30=z/(1500+z/(tan 34))

    This is a regular equation for z.
    ---
    Alterntiely you can dived your equations,
    tan 30/tan 34=x/(1500+x)
    Solve for x,
    Then solve for z
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