If point A is in equilibrium under the action of the applied forces, the values of tension. T_AC = ?

Concept:

Lami's theorem:

It states that if three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two forces. Consider three forces FA, FB, FC acting on a particle or rigid body making angles α, β and γ with each other.

Therefore, \(\frac{{{F_A}}}{{sin\ \alpha }} = \frac{{{F_B}}}{{sin\ \beta }} = \frac{{{F_C}}}{{sin\ \gamma }}\)
Calculation:

Given:

We have angle BAC = 180° - (30° + 60°) = 90°

angle BAC = 90°

By Lami’s Theorem,

\(\frac{{{800}}}{{sin~90°}} = \frac{{{T_{AC}}}}{{sin~150° }}\)

TAC = 400 N