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Math Help - Height question involving angle of elevation and angle of depression

  1. #1
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    Height question involving angle of elevation and angle of depression

    Hi, I really do not understand this question, if you could please solve and explain it, I would greatly appreciate it!



    Here it is:

    The angle of elevation of the nearby taller building is 56.5 degrees and the angle of depression to the bottom of the taller building is 18.3 degrees. If the short building is 50.2 meters high, what is the height?


    Thanks so much!
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  2. #2
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    (sorry about bad drawing - my GIMP skills are hopeless)

    But yeah, that hopefully explains depression and elevation. Looking up from the direct line - that is the horizontal area that is 0 degrees is the elevation point (so it's out of proportion on my picture).

    Now Height X is equal to 50.2 metres (which is given in the question). From there and using the angle of depression we can find the distance between the two buildings. Which is found by (using tangent = opposite/adjacent):

    Code:
    tan(18.3) = (distance between buildings)/50.2
    
    = tan(18.3) * 50.2 = 16.6021
    With that found you can now find Y. Again, it's found like this:

    Code:
    tan(56.5) * 16.6021 = y
    
    y = 25.083
    Then you add the values of X and Y to get the height of the building. Perhaps round it down - but yeah.

    Check my numbers, but hopefully you understand the concept. Be sure to add the measurement units to your answer. Often a diagram will help with the problem
    Last edited by Rudey; March 28th 2009 at 02:52 AM. Reason: more information
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  3. #3
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    Your drawing doesn't show the angle of depression.

    Angle of depression is the angle between the horizontal and the line of sight to an object beneath the horizontal.


    Distance between the buildings is about 151.8 m.

    I like the image.
    What is GIMP?
    (I'll google it.)
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