Lami's theorem

In physics, Lami's theorem is an equation relating the magnitudes of three coplanar, concurrent and non-collinear vectors, which keeps an object in static equilibrium, with the angles directly opposite to the corresponding vectors.

are the magnitudes of the three coplanar, concurrent and non-collinear vectors,

, which keep the object in static equilibrium, and

α , β , γ

are the angles directly opposite to the vectors,[1] thus satisfying

α + β + γ =

Lami's theorem is applied in static analysis of mechanical and structural systems.

The theorem is named after Bernard Lamy.

[2] As the vectors must balance

, hence by making all the vectors touch its tip and tail the result is a triangle with sides

α , β , γ

are the exterior angles).

By the law of sines then[1]

Then by applying that for any angle

− θ ) = sin ⁡ θ

(supplementary angles have the same sine), and the result is

sin ⁡ α

sin ⁡ β

sin ⁡ γ