The members of a truss are pin connected at joint O. Determine the magnitude of F_1 and its angle ϴ for equilibrium. Set F_2 = 6 kN.
In the previous solution, we solved the question using unit vectors. In this solution, we will avoid using them.
(unit vectors are not necessary to solve these questions, however, they help a lot when dealing with questions involving the z-axis).
Let us first draw the free body diagram with the values given to us in the question like so:
We will also assume \rightarrow^+ is positive and \uparrow+ is positive.
Now, let us write the forces in the x-axis domain as follows:
(isolate for F_1)
Now, we can write the forces in the y-axis domain as follows:
(simplify by solving the trigonometric values)