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.

#### Solution:

### 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:

### \sum \text{F}_\text{x}=0

### 6\text{sin}\,60^0\,+\,F_1\text{cos}\,\theta \,-\,5\text{cos}\,30^0\,-\,7(\frac{4}{5})\,=\,0

##### (isolate for F_1)

### F_1=\frac{4.734}{\text{cos}\theta}

### Now, we can write the forces in the y-axis domain as follows:

### \sum \text{F}_\text{y}=0

### 6\text{cos}\,60^0\,-\,F_1\text{sin}\,\theta \,+\,5\text{sin}\,30^0\,-\,7(\frac{3}{5})\,=\,0

##### (simplify by solving the trigonometric values)

### F_1\text{sin}\,\theta \,=\,1.3