# How to find maximum change in the following scenario?

1. Feb 19, 2012

### PatternSeeker

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.