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How to find maximum change in the following scenario?

  1. Feb 19, 2012 #1
    I need directions regarding methods that I could use for the following type of problem:

    I am given the following scenario:

    Observers consistently estimate objects as 20% shorter than they really are in the "y" dimension. They accurately estimate objects in the "x" dimension.

    ** error in estimated lengths in the y dimension, % error y = -20 % of physical lengths.
    ** error in estimated lengths in the x-dimension, % error x = 0% of physical length

    Observers also consistently overestimate physical angles between "x" dimension and directions between "x" and "y" dimension.

    Let physical angle = σ
    Let estimated angle = β

    ** angle β = arctan ((sin α (% error x + 100))/(cos α ( % error y + 100))

    *** Angles α and β vary between 0 deg to 90 degrees. The change between the
    two is not constant, however. It will be greatest at a particular value of angle α.

    QUESTION: If the physical length y is underestimated by 20 %, at which physical angle α
    (between 0 and 90 degrees) will the change between angle β and angle α be
    the greatest?

    How would you suggest I approach this problem? Should I use differential calculus?

    By the way, my background in math is pretty basic - I took undergraduate calculus a few years ago.
  2. jcsd
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