Calculating Moment Generated by P on a Gate | Trigonometry Triangle Help

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The moment generated by force P is calculated using the formula PLsin(θ), where L is the length and sin(θ) represents the perpendicular distance from the pivot point to the line of action of the force. The confusion arises from understanding that sin(θ) applies to the distance L, not the force P itself. When constructing the force triangle, it's essential to visualize the moment vector's direction, which acts opposite to the applied force F. The moment is defined as the product of force and the perpendicular distance from the pivot point. Properly applying these principles will clarify the calculation of the moment.
GBE111
Could someone please explain to me how the moment generated by P is calculated by PLsin@. I understand the length I just can't figure out how it is Psin@. I believe the moment acts opposite to force F but when I build my triangle for trigonometry I'm getting it wrong?
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I moved your thread from ME to the schoolwork forums.

Can you show us your force triangle? When gravity acts vertically on that rod, in which direction is the moment vector on it?
 
L*sin(theta) is the perpendicular distance (lever arm) of force P about point B. Sin(theta) "acts" on the distance L, not the Force.

Moment = Force ( Cross Product) Distance in 3D
Moment = Force * Perpendicular distance in 2D
 

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