Rotation matrices are somewhat mysterious to the uninitiated, but so is matrix multiplication until it "clicks". Whether it ever clicks is a function of the quality of the learning resource (I certainly do not recommend trying to learn linalg via 3D graphics by just dabbling without a good graphics-oriented textbook or tutorial – that usually doesn’t end well).

Anyway, I believe that it's perfectly possible to explain rotation matrices so that it "clicks" with a high probability, as long as you understand the basic fact that (cos a, sin a) is the point that you get when you rotate the point (1, 0) by angle a counter-clockwise about the origin (that's basically their definition!) Involving triangles at all is fully optional.