How do you determine resultant force in physics?

You have to know the magnitude and direction of the individual forces. Let's say you have 3 forces acting on a body.
F1 = 45 N at 45°F2 = 60 N at 120°F3 = 75 N at 270°
Now you have to resolve the forces into their horizontal (x) and vertical (y) components.
F1 = <45 cos 45°, 45 sin 45°> N = <31.8, 31.8> NF2 = <60 cos 120°, 60 sin 120°> N = <-30, 52> NF3 = <75 cos 270°, 75 sin 270°> N = <0, -75> N
Add the horizontal component (1st number) of each force to find the horizontal component of the resultant force (Fx).
Fx = 31.8 N + (-30 N) + 0 N = 1.8 N
Do the same with the vertical components to find Fy.
Fy = 31.8 N + 52 N + (-75 N) = 8.8 N
Now find the magnitude of the resultant force


Now find the direction of the resultant force. 


The next thing you should do is figure out which quadrant the resultant force is in. The arctan function only has a range from -90° to 90°, so if the force is outside the first quadrant you'll have to use your knowledge of reference angles to find the corresponding angle between 0° and 360°

We have a positive Fx and a positive Fy, so F is in the first quadrant, and 78.4° is the correct angle.

The resultant force is 8.98 N at 78.4°.

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