Finding some connection between trigonometry and angles of rubber-powered trebuchets is incidental and quite frankly, this approach isn't going to take you very far. One simply can't find real world mappings to atleast 99% of what is properly called math. Even if you'd like to strictly operate within the confines of high school geometry , it is a study of points, lines, planes, angle relations, norms & distances motivated by axioms & theorems that follow by symbol pushing. For example, it so happens that if you push the right symbols, you'll eventually work out that the area of a triangle is related to its sides ( http://en.wikipedia.org/wiki/Herons_formula ). But this is a consequence of your definition of area and triangle and side and so forth. The relationship falls out of those definitions. Its not about constructing a real wooden triangle out of real sticks & then measuring its area and then the lengths of its sticks and saying - hey, I told you so! Those things ie. the real wood and the real sticks,...reality - is just a sideshow. Real world problems are at best a distraction. If you were to focus only on these sort of real-world mappings, you'd end up as an accountant - because that's were 1 would map to $1, 2to $2 and add would mean 1 + 2 = $3 and so forth. That's what corresponds to reality and the real world. That isn't math. Math is where you say 1 + 2 = 0 because the abelian group G3 with three elements {0,1,2} can satisfy the addition rule and have three distinct elements only if 1 + 2 was 0. For if 1 + 2 was 1, then that would mean 2 was equal to zero by cancelation laws. Similarly if 1+2 was 2 then 1 would equal 0. Since you do have 3 elements, it stands to reason that 1+2 must be 0, because it can't be anything else in that system. That's math.