Question

1. Determine the magnitude of the resultant force acting on the plate and its direction, measured counter-clockwise from the positive x axis.
F1 = 900 N
F2 = 750 N
F3 = 650 N





A diagram is attached to this question.

Answer 1

F1 . . . 100% of it = 900N is in the +x direction.

F2 . . . 70.7% of it (cos45°, 530.3N) is in the +x direction,
and 70.7% of it (sin45°, 530.3N) is in the +y direction.

F3 . . . 80% of it (520N) is in the -x direction,
and 60% of it (390N) is in the +y direction.

Total x-component:  900 + 530.3 - 520  =  1,950.3 N

Total y-component:  530.3 + 390  =  920.3 N

Magnitude of the resultant = √ (x²  +  y²)

                                       = √(1950.3²  +  920.3²)

                                       =  √4,650,070.09

                                       =   2,156.4 N  .

Angle of the resultant, measured counterclockwise
from the +x axis, is 
 
                               tan⁻¹  (y / x)

                         =    tan⁻¹  (920.3 / 1950.3)

                         =    tan⁻¹  (0.4719)

                         =    about    25.3°  .

Caution:
The same fatigue that degrades my ability to READ the question accurately
may also compromise the accuracy of my solutions.  Before you use this
answer for anything, check it, check it, check it !