This is a demonstration of a coordinate transformation tools that I use in my mechanics (Statics & Dynamics) classes. Enjoy!
Cite this work as:
Julian L. Davis (2020), "Coordinate Transformation Tool," https://www.handsonmechanics.org/statics/819.
Hands-On Mechanics
This tool would undoubtedly help students practice finding angles. But to internalize their understanding and so graduate from needing the tool, I think that all they need to learn is this:
Suppose that two lines form an angle (hold up two fingers of one hand to form a V), and two other lines form another angle (hold up two fingers of the other hand to form another V). If each line in one pair (wiggle fingers of one V) is perpendicular to a line in the other pair (wiggle fingers of the other V), then both pairs of lines form the same angle.
With this knowledge, a student can easily find the angle between an incline (or normal to the incline) and the horizontal or vertical when the incline (or normal) makes a known angle with either horizontal or vertical.