SOLUTION: Two forces act on a point on the plane. The angle between the two forces is given. Find the magnitude of the resultant force. forces of 19 and 32 newtons, forming an angle of 11

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Question 687793: Two forces act on a point on the plane. The angle between the two forces is given. Find the magnitude of the resultant force.
forces of 19 and 32 newtons, forming an angle of 118 degrees.
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!

We will pick the 19 N force to be at angle 0° for convenience:

           Magnitude   Angle       x-component        y-component
----------------------------------------------------------------------
Force 1      19N         0°      19cos0°=  19         19sin0° = 0
Force 2      32N       118°    32cos118°= -15.023   32sin118° = 28.254
----------------------------------------------------------------------
                                   SUM =    3.977         SUM = 28.254

                             Resultant = sqrt%283.977%5E2%2B28.254%5E2%29
                                       = 28.533 N

We can also use the law of cosines (but use the supplement of the angle):

R² = 19² + 32² - 2(19)(32)cos(180°-118°)
R² = 361 + 1024 - 1216cos(62)
R² = 814.1225797
 R = √814.1225797
 R = 28.533N

Edwin