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State & prove Lami's theorem.

It's very useful app for engineering students


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Lami's theorem states that, if three concurrent forces act on a body keeping it in Equilibrium, then each force is proportional to the sine of the angle between the other two forces.

Let P, Q, R be the 3 concurrent forces in equilibrium as shown in fig. (a)

Since the forces are vectors, we can move them to form a triangle as shown in fig. (b)

enter image description here

Applying sine rule we get

$P/(\sin (180 -\alpha)) \\ =Q/(\sin(180-\beta))\\ =R/(\sin(180-\theta)) \\ \\ P/ (\sin \alpha)\\ =Q/ (\sin \beta)\\ =R/(\sin \theta) ...... \text { Hence Proved}$

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