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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?

Thanks in advance.

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    $\begingroup$ Things would be a lot clearer with a drawing $\endgroup$
    – Mister Mak
    May 13, 2021 at 10:19

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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 $Lcos \theta$.

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

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