Determine the magnitude of the resultant force by adding the rectangular components of the three forces.

 Determine the magnitude of the resultant force by adding the rectangular components of the three forces.

Solution:

First, we must add/ sum up all the forces for x-components. That is...

Fx(Rx)= F1x + F2x + F3x (since F3 is parallel to y-axis,F3x=0)
= -50cos30 + 75cos45 + 50cos90
Fx(Rx)= 9.7317...N

Then, add/sum up all the forces for y-components.

Fy(Ry)= F1y + F2y + F3y
= 50sin30 + 75sin45 - 50sin90
Fy(Ry)= 28.03300...N

R=*squareroot of [(Ry)^2 + (Rx)^2]
=*suareroot of [(28.03300859 N)^2 + (9.7317384 N)^2]
R=29.67416895 N

θ= arctan [Ry/Rx]
= arctan [28.03300859/9.7317384]
θ= 70.86 degrees

Therefore, the answer is 29.67416895 N