A definition is whatever you want it to be. The standard definition of sin([itex]\theta[/itex]), where [itex]\theta[/itex] is an angle in a right triangle, is "length of the leg opposite angle [itex]\theta[/itex] divided by the length of the hypotenuse", which is, I guess, what you meant by "vertical". If you meant why it was defined that way, then the only reasonable answer is "because that definition helps to solve many practical problems involving right triangles".
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