What is the magnitude of the torque τ on the pole, about point a, due to the tension in the rope?

Answer
Using trigonometry, the lever arm is Lcosθ.

(The ‘lever arm’ is the perpendicular distance from A to the line of action of the tension. It corresponds to the distance from A to where the rope is attached to the wall.)

So the magnitude of the torque is TLcosθ.