I believe that angles have a dimension. The ratio theory is simply wrong. While I have a longer description, here is a summary. I'd like feedback on whether this makes sense, and whether giving it a dimension works with the various formulas that you might use in your work.
First a question...
Quickly estimate the value of this expression: sin(1.57). If your answer was about 1, then you assumed that 1.57 was a radian value. If your answer was about 0, you assumed that 1.57 was degrees. If you said that you can’t determine an answer, then you were expecting to see an angle...