Opposite Side
The opposite side in a right triangle is the side directly across from a given reference angle.
Definition
In a right triangle, the opposite side is the side directly across from the angle you are looking at, the leg that does not touch that angle and is not the hypotenuse. It appears in the sine ratio, $\sin(\theta) = \text{opposite}/\text{hypotenuse}$. More generally, for an angle $\theta$ in standard position, the opposite side is the perpendicular projection of the terminal side onto the $y$-axis, equal to $r\sin(\theta)$ where $r$ is the radius; on the unit circle ($r = 1$), $\sin(\theta)$ is literally the length of the opposite side of the reference triangle.
Example
If you are standing at a $35$-degree angle in a right triangle, the wall directly in front of you is the opposite side. In a $30^\circ$-$60^\circ$-$90^\circ$ triangle with hypotenuse $2$, the side opposite the $30^\circ$ angle has length $1$, so $\sin(30^\circ) = 1/2$; likewise, for $\theta = \pi/3$, the opposite side of the $30$-$60$-$90$ reference triangle is $\sqrt{3}/2$, confirming $\sin(\pi/3) = \sqrt{3}/2$.
Key Insight
The label "opposite" always depends on which angle you pick, switching to a different angle changes the opposite side, which is why SOH-CAH-TOA must always reference a specific angle before labeling the sides. The abstraction from "opposite side of a triangle" to "$y$-coordinate on the unit circle" is the key conceptual leap that extends sine beyond acute angles to all real numbers.