What is the x component, the y component, the magnitude, and the angle of the third force?

Question

An object at rest has three forces acting on it. The first force is 129 N acting along the positive x-axis. The second force is 159 N acting at an angle of 20 degrees relative to the positive x-axis.

Answer 1

Trigonometry is your friends. The X component of the second force is 159 * cos (20 degrees). The Y component is 159 * sin (20 degrees). The X and Y components of the first force are 129 and 0 respectively.

Add, and you have the X and Y components of the third force.

The magnitude is the square root of the sum of the squares of the X and Y components.

Divide the X and Y components by the magnitude, take the arccosine and arcsine, and both times you should get the angle. (If the two numbers equal, that's a good check that you may have done the problem correctly.)