The pole is subjected to the force F which has components F_x= 1.5 kN and F_z= 1.25 kN. If β =75°, determine the magnitudes of F and F_y.

#### Solution:

### To do this question, we have to remember the following equation:

### \text{cos}^2\alpha +\text{cos}^2\beta +\text{cos}^2\gamma =1

### Looking at the diagram and the values given to us in the question, we can write \text{cos}\,\alpha as \frac{1.5}{F}.

### We also know from the question that \beta=75^0.

### Similar to before, we can write \text{cos}\,\gamma as \frac{1.25}{F}.

### Let us substitute these values into our equation like so:

### (\frac{1.5}{F})^2\,+\,\text{cos}^{2}(75^0)\,+\,(\frac{1.25}{F})^2=1

### Solving for F gives us:

### F= 2.02 kN