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

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SUMMARY

The moment generated by force P on a gate is calculated using the formula Moment = P * L * sin(θ), where L is the length of the lever arm and θ is the angle between the force and the lever arm. The perpendicular distance from the pivot point to the line of action of the force is represented by L * sin(θ). This calculation is crucial for understanding the mechanics of forces acting on structures, particularly in two-dimensional scenarios. The moment vector acts in the direction opposite to the applied force F.

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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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