In terms of a right triangle, if y is the opposite side, what does sin equal?

In a right triangle, the sine (sin) of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. In this case, if ( y ) represents the length of the opposite side, and ( r ) represents the length of the hypotenuse, then the sine function for that angle can be expressed as:

[

\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{y}{r}

]

This is why the correct answer is ( \frac{y}{r} ). It accurately represents the relationship defined by the sine function within the context of a right triangle.

Other choices might represent different trigonometric ratios or be based on incorrect relationships that do not match the definition of sine in relation to the opposite side and the hypotenuse.