Ratios of sides in a right triangle are always trigonometric functions of its angles.Ah.You said just a ratio.From where did this FUNCTION come.

Why is that a ##\tan^{-1}##? Can the ratio of a cathetus with the hypotenuse be a ##\tan##?Anyway,I know what you mean.

It's ##\gamma=tan^{-1}(\sin\alpha\cos\beta)##