Investigating the Relationship Between Shadow Length and the Angle of Elevation Using Trigonometric Modeling and Related Rates

This investigation explores the mathematical relationship between the angle of a light source and the resulting shadow length. Using primary data collected from a controlled experiment with a torch and a cuboid object, the student models the relationship using exponential, reciprocal, and trigonometric functions.

The cosecant function is identified as the superior model due to its ability to accurately represent asymptotic behavior and periodicity. Furthermore, the paper applies calculus through related rates to determine how the shadow length changes relative to the angle of elevation, assuming Earth's rotational rate. The work is distinguished by its rigorous application of the quotient rule and a critical evaluation of systematic experimental errors.