How did you draw an extension of the force to find $r$ perpendicular to it?

To find the ``line of the force'', just take the direction of the force, and draw a line along it. Then, go to the pivot point, and drop a perpendicular to the line of the force. The distance between the pivot point and the line of the force is $r_\perp$, and it's called the ``lever arm'' or ``moment arm''. With a little geometry, you can see that $r_\perp = \vert\vec{r}\vert\sin \theta$. So you can write the magnitude of the torque as $\vert\vec{\tau}\vert = \vert\vec{r}\vert\vert\vec{F}\vert\sin\theta = Fr_\perp$: it's the magnitude of the force times the lever arm.