In this situation, the directions of all four forces are specified by the angles in the free-body diagram, and the magnitude of the weight is known. The three unknowns are the magnitudes of forces and
We will first find unit vectors in the directions of the four forces by inspection of the free-body diagram. This step requires visualizing the component’s unit vectors and determining the angles each makes with the coordinate axis.
Particle equilibrium requires that
This is a 3 3 system of three simultaneous equations, one for each coordinate direction, which needs to be solved for and
These can be solved by any method you choose. Here we will use Sage. Evaluating the coefficients and expressing the equations in matrix form gives
This is an equation in the form
Entering the coefficient matrices into Sage.
After evaluating, we learn that
.