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Math Help - Basic Trig Word Problem

  1. #1
    Newbie LaMandie's Avatar
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    Basic Trig Word Problem

    " From point A, the angle of elevation to the top of a building is 32. Walking 70m closer, the angle changes to 44. How high is the building?"

    So far, I've gotten this:
    xtan44 = (x + 70)tan32

    Each time I try it though, I get completely different answers.
    All I need is for someone to just do it themselves while showing how they did it.
    Thankyou very much!
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  2. #2
    Super Member

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    Hello, LaMandie!

    Show us your work for your different answers.

    And we can tell you where you made errors.

    Isn't that easier for all of us?

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  3. #3
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    Since the height of the building at either point should be the same we get the equality

     xtan(32) = (x-70)tan(44)_{.}

    Expanding the R.H.S. of the equation and rearranging to make x the subject, we get

    x = \frac{70tan(44)}{tan(44)-tan(32)}_{.}

    See what this comes out as on your calculator.
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  4. #4
    Newbie LaMandie's Avatar
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    Alrighty then!

    1. xtan44 = (x + 70) tan32
    x0.9657 = (x + 70)0.6249
    x0.9657 = x0.6249 + 43.7409
    x = x0.6249 + 43.7409 / 0.9658
    x = x0.6249 + 45.2898
    1 = 0.6249 + 45.2898
    1 = 45.9147

    2. xtan44 = (x + 70) tan32
    x = (x + 70) tan32/tan44
    x = ( x + 70) 0.6471
    x = 0.6471x + 45.295
    1 = 29.3104

    3. xtan44 = (x + 70) tan32
    xtan44 / tan 32 = (x + 70)
    x1.545 = (x + 70)
    1.545 = (x + 70) / x
    1.545 = 70

    4. xtan44 = (x + 70)tan32
    xtan44 = xtan32 + 70tan32
    x = xtan32 + 70tan32 / tan44
    1 = tan32 + 70tan32 / tan44
    1 = 43.4
    Last edited by LaMandie; November 21st 2010 at 05:53 PM. Reason: To add more of the work I did
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  5. #5
    Newbie LaMandie's Avatar
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    willy, thanks for the help! The answer is right -only I don't really get how you got 70tan44 / (tan44 - tan32).
    Could you explain this for me please? Thanks a bunch!
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  6. #6
    MHF Contributor harish21's Avatar
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    I'll give you the steps.. hope you can draw the picture..

    Draw a right angled triangle ABC, where angle B=90 degrees.. AB is the height of the building..

    angle ACB=32 degrees and BC is the base of the triangle. suppose that the length of BC=x..

    if you move 70m close to the building from pint C, then the angle is 44 deg.

    so there is a point D on the line BC such that angle ADB=44 deg..

    Also, since BC = x, and CD=70m, you have BD=(x-70)m

    so,
    \tan 32=\frac{AB}{BC}=\frac{AB}{x}.....(I)

    and

    \tan 44=\frac{AB}{AD}=\frac{AB}{x-70}......(II)

    from (I), you have AB = x \times \tan 32

    and from (II), you have AB = (x-70) \times \tan 44

    so, you have:

    x(\tan 32 = x(\tan 44)-70(\tan 44)

     70(\tan 44) = x(\tan 44)-x(\tan32)

    70(\tan 44)  = x (\tan 44 -\tan 32)

     x = \dfrac{70(\tan 44)}{\tan 44 -\tan 32}

    then substitute the value of x in equation (I) to find AB
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  7. #7
    Newbie LaMandie's Avatar
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    Thanks a bunch!
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