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Thread: I need a detailed way to solve a problem I'm not getting.

  1. #1
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    I need a detailed way to solve a problem I'm not getting.

    The problem is "From the top of a building 21m tall the angle of elevation to the top of a taller building is 46 degrees. The Angle of depression to the base of the taller building is 51 degrees. How tall is the other building?"
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  2. #2
    MHF Contributor
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    Re: I need a detailed way to solve a problem I'm not getting.

    Draw a diagram.

    I need a detailed way to solve a problem I'm not getting.-building.png

    Note that you can determine the distance between the buildings using the definition of the tangent of an angle in the lower right-angled triangle.
    This then gives you enough to determine the additional height of the taller building using the upper right-angled triangle.

    Edited to correct the diagram.
    Last edited by Archie; Aug 30th 2018 at 07:01 PM.
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  3. #3
    MHF Contributor

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    Re: I need a detailed way to solve a problem I'm not getting.

    You have two right triangles so trigonometry will work nicely. You are given the two angles DAE and EAC. There is a little bit of a "catch" here in that you are not given, directly, the distance between the two buildings, AE. However, the distance CE is the same as the distance AB, the height of the first building, 21 m. You can use right triangle ACE to determine distance AE.
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