Identify the angle and the sides of the right-angled triangle.

Step 1: Identify the angle and the sides of the right-angled triangle. The angle in question is $\theta$. The sides are labeled $r$, $s$, and $t$. Side $t$ is the hypotenuse, as it is opposite the right angle. Sides $r$ and $s$ are the perpendicular sides (legs) of the triangle.

Step 2: Determine which perpendicular side is adjacent to $\theta$. The side opposite to angle $\theta$ is $s$. The side adjacent to angle $\theta$ (and not the hypotenuse) is $r$.

The perpendicular side adjacent to the angle $\theta$ is $r$.

$\boxed{\text{*r*}}$