Calculating Moment of Force Produced at Point A

[musicmar]

Homework Statement

In order to raise the lamp post from the position shown, force F is applied to the cable. If F = 200 lb, determine the moment produced by F about point A. I've attached the diagram. I apologize for the terrible quality. The length of the post from A to B is 20 ft.

The Attempt at a Solution

M_A=Fd
=200 lb (cos 75) (20 ft) = 1035.3 ft-lb

I think I somehow reasoned that the angle between AB and AC is 15°, so its complement is 75°. I said that the component of the force acting perpendicular to the moment arm is 200 cos 75. I know this is backwards from what it is supposed to be. It should be the force times the perpendicular component of the moment arm. I'm not sure that it matters much here, but I don't know how to describe the perpendicular moment arm.


Thank you.

 

[cupid.callin]

I think I somehow reasoned that the angle between AB and AC is 15°, so its complement is 75°.

Total angle is 180 degree not 90 degree

 

[musicmar]

I meant between F and an imaginary line perpendicular to the post at B, so the angle there would be 75 degrees. I don't think that's where my mistake is. If anything, it's what these angles mean.