Choose an axis system as shown and write the two vectors in Cartesian notation. It is important that the correct sign is used.

     F₁ = 0i - 500j  lb

     F₂ = 500 sin30i - 500 cos30j  lb

         = 250i - 433j  lb

Addition of Forces Diagram  

Now that the two vectors are described using the unit vectors, i and j, they can been easily added. Adding the two forces will give the total force in Cartesian notation,

     F_R = F₁ + F₂ = 250i - (500 + 433)j

         = 250i - 933j  lb

The magnitude of the total force can be determined by squaring the i and j magnitudes, and then taking the square root,

     F_R = (250² + 933²)^0.5 = 965.9 lb

The angle at which the total force acts is,

     θ = tan^-1 (250/933) = 15^o