How to Calculate Equivalent Torque Distance on a Pivoting Rod?

[PrideofPhilly]

Homework Statement

A rod can pivot at one end and is free to rotate without friction about a vertical axis. A force F is applied at the other end, at an angle theta to the rod. If F were to be applied perpendicular to the rod, at what distance d from the axis of rotation should it be applied in order to produce the same torque t?

Homework Equations

t = rF

The Attempt at a Solution

My answer: d = Lsin(theta).

Is that correct or am I missing something?

 

[LowlyPion]

If the force is applied horizontally this would be true.

When the angle is 90 degrees the force would be fully engaged in developing torque at that displacement.