How does one solve this?

Question

Suppose a body has a force of  pounds acting on it to the right,  pounds acting on it  from the horizontal, and  pounds acting on it directed  from the horizontal. What single force is the resultant force acting on the body? Round answers to 2 decimal places.

Answer 1

A problem like this is most easily solved by adding the components of the forces to find the x and y components of the resultant force. Then, the pythagorean formula is used to find the resultant force and trigonometry is used to find the direction of the resultant.

R_x = 20(cos 0º) + 5(cos -125ºº) +5(cos 145º) = 13.04

R_y = 20(sin 0º) + 5(sin -125º) +5(sin 145º) = -1.228

R =(R_x² + Ry²)^0.5 = 13.09 lb

θ = tan^-1(R_y/R_x) = -5.38º