Lami's theorem states that if three coplanar concurrent forces are acting on an object and the object is in equilibrium, then the ratios of the magnitudes of the forces to the sines of angle between the other two are equal.
m_A = mass of bottle A with water. V_A = volume of water in the bottle.
One can take two strings of lengths like mentioned in the diagram and tie them together. Then pass them over some nails or hooks. Hang some weights like filled water bottles tying the strings to their necks. Hold the weights carefully and when they seem to balance, release them. u can pour more water a bottle or two if necessary to balance them as shown.
Measure the angles at the middle point using a protractor. Then compute the Sine values. Know the weight by knowing the amount of water - mass. Then verify the theorem.
I have mentioned some sample weights and lengths. change them as per your experiment.
Note down the lengths of the sides OD, OE, DE. See if the lengths follow the Sine rule, when the weights are balanced.