# Which out of sine and cosine do you use when calculating the moment of a force?

For some reason I've never been able to get my head around when to use sine or cosine with angles. I recently thought I'd sussed it, but calculating moments about a point has got my head in a spin (pardon the pun).

I'm looking at a question with 2 ladders of equal length $$2L$$ leaning against each other. I'm taking moments about the base $$A$$ of one of the ladders, which makes an angle $$\theta$$ from the ground, and we have the weight $$W$$ acting vertically downwards.

The perpendicular distance then between A and the line of the vertical force is surely the base of the right triangle.. which is the adjacent side to the angle $$\theta$$, and therefore should be the cosine multiplied by hypotenuse, i.e $$\cos \theta L$$. So the moment would be $$\cos \theta L W$$.

But I've seen various places online using the sine of the angle in this scenario.

Would I be right to use the cosine for this perpendicular length or am I missing something?

• Things would be a lot clearer with a drawing May 13, 2021 at 10:19

Yes, magnitude if torque is given by $$\tau=r_{\bot}F$$, where $$r_{\bot}$$ represents perpendicular distance between force and point about which torque is being calculated, so in this case you will use $$Lcos \theta$$.

• Great, thanks for the confirmation.
– Jbo
May 13, 2021 at 10:14