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.