The bolt is subjected to the force F, which has components acting along the x, y, z axes as shown. If the magnitude of F is 80 N, and α=60° and γ=45°, determine the magnitudes of its components.

#### Solution:

### To solve this question, we will have to use the following equation.

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

### We will now isolate for \text{cos}\beta.

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

### As stated in the question, we will now substitute the values given to us.

### \text{cos}\beta =\sqrt{1-\text{cos}^{2}60^0-\text{cos}^{2}45^0}

### Solve for \beta.

### \beta=120^0