Why do trigonometric ratios have to be related to the angle between the base and hypotenuse of a right angle triangle? I am trying to understand why I can't use these ratios to any angle of a right angle triangle. I try to do that in the attached document. It seems to work for all ratios except cos90 and tan90. I know the origin of the trigonometric ratios is in the unit circle and the length of the cord, but why can't we extend this principal to any angle of a right angle triangle? Thanks.