# Lami's theorem

(Redirected from Triangle of forces)

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

${\displaystyle {\frac {A}{\sin \alpha }}={\frac {B}{\sin \beta }}={\frac {C}{\sin \gamma }}}$

where A, B and C are the magnitudes of the three coplanar, concurrent and non-collinear forces, ${\displaystyle F_{A},F_{B},F_{C}}$, which keep the object in static equilibrium, and α, β and γ are the angles directly opposite to the forces.[1]

Illustration of Lami's theorem

Lami's theorem is applied in static analysis of mechanical and structural systems. The theorem is named after Bernard Lamy.[2]

## Proof

As the forces must balance ${\displaystyle F_{A}+F_{B}+F_{C}=0}$, hence by making all the forces touch its tip and tail we can get a triangle with sides A,B,C and angles ${\displaystyle 180^{o}-\alpha ,180^{o}-\beta ,180^{o}-\gamma }$. By sine rule,[1]

${\displaystyle {\frac {A}{\sin(180^{o}-\alpha )}}={\frac {B}{\sin(180^{o}-\beta )}}={\frac {C}{\sin(180^{o}-\gamma )}}}$

${\displaystyle \therefore {\frac {A}{\sin \alpha }}={\frac {B}{\sin \beta }}={\frac {C}{\sin \gamma }}.}$