Question

An object in equilibrium has three forces exerted on it. a 42 n force acts at 90° from the x-axis and a 46 n force acts at 60° from the x-axis. what are the magnitude and direction of the third force? n ° (counterclockwise from the +x direction)

Answer 1

Since the object is in equilibrium, then the sum of the forces acting on it is zero. You must do the sum of forces for the component "y" and for the component "x". From there you clear the components of the third force. Then you must find the direction and magnitude.
The result is a force of 85.01N at 74.30 degrees from the x axis. Attached solution.