Consider the torque from a force exerted on a hinged rod about the hinge, as shown in the diagram. The torque points out of the screen, corresponding to counterclockwise motion.

There are three equivalent ways to determine the magnitude of the torque:

Method 1: Measure r from the hinge along the rod to where the force is
applied, multiply by the force, and then multiply by the sine of the angle
between the rod and the force. This gives: τ = r F sin θ

Method 2: Resolve F into components perpendicular to and parallel to the
rod. The parallel component produces no torque. The perpendicular component,
Fsin θ, gives a torque of magnitude:
τ = r [Fsin θ ] = r F sin θ

Method 3: Extend the line of the force and measure the lever arm r' = r sin θ , the prependicular
distance from the rotation axis to the line of the force. The magnitude of
the torque then is:
τ = r' F sin 90 = r' F = r F sin θ