A line make angle `60^(@) and 45^(@)` with the positive direction of x-axis and y-axis repectively. What acute angle does it make with the z-axis?

Explanation

To find the acute angle that a line makes with the z-axis when it makes angles of \(60^\circ\) with the x-axis and \(45^\circ\) with the y-axis, we can use the relationship between the angles and the direction cosines of the line.

### Step-by-step Solution:

1. **Understanding Direction Cosines**:
The direction cosines of a line are given by:
\[
l = \cos(\alpha), \quad m = \cos(\beta), \quad n = \cos(\gamma)
...