How do I find the magnitude and direction of a force?

Question

One force of 100 units acts upon an object. Another force of 80 units acts upon the object at a 40° angle from the first force.

Answer 1

Assuming the 400 unit force acts in the x-direction, the components of the net force are

 

F_x = (100 + 80cos40°) units = ? units

F_y = 80sin40° units = ? units

 

The magnitude of the net force is

 

F = √(F_x² + F_y²)

 

Its direction above the horizontal is

 

θ = tan^-1(F_y/F_x)

 

Plug in the the numbers and finish from here.