My second career having been in education, I think I am qualified to look back and say that most (not all) of my high school teachers and college professors were pretty poor teachers. When I was in high school, I barely made it through. I'd been forced to take all the math offered with no idea why. After the Navy, when, when I got into my tool and die apprenticeship, we had classes in such things as trigonometry and solid geometry. We'd study the stuff in class and go out in the shop and apply it. Suddenly it all made sense. Setting up compound angles on a magnetic sine chuck to grind a form tool brought it all into focus for me.
In later years, when I taught that stuff, I'd always begin teaching trigonometry by telling the students, "You can always trust a triangle." That statement got their attention and served as a good jumping off point for why we use trigonometry.
