FORCE TRIANGLE 23 



Ps 



(C) 



The value of R may also be found from the equation 

 R* = PS + P 2 * + 2 P, P 2 cos 



It is not necessary to construct the entire force parallelogram as 

 in (a) Fig. 8, the force triangle (b) below or (c) above the resultant R 

 being sufficient. 



If only one force together with the line of action of the two others 

 be given in a system containing three forces in equilibrium, the magni- 

 tude and direction of the two forces may be found by means of the 

 force triangle. 



If the resultant R in Fig. 8 is replaced by a force H equal in 

 amount but opposite in direction, the system of forces will be in equi- 

 librium, (a) or (b) Fig, 9. The force H is the equilibrant of the system 

 of forces P^ and P 2 . 



It is immaterial in what order the forces are taken in constructing 

 the force triangle, as in Fig. 9, as long as the forces all act in the same 

 direction around the triangle. The force triangle is the foundation 

 of the science of graphic statics. 



