If a line make angle `30^@` and `60^@` with the x and y axes, what angles does it make with the z axes?

Explanation

To solve the problem, we need to find the angle that a line makes with the z-axis given that it makes angles of 30° with the x-axis and 60° with the y-axis. We can use the relationship between the angles and the direction cosines.

### Step-by-step Solution:

1. **Understanding Direction Cosines**:
The direction cosines of a line making angles \( \alpha \), \( \beta \), and \( \gamma \) with the x, y, and z axes respectively are given by:
\[
\cos \alpha = l, \quad \cos \beta = m, \quad \cos \gamma = n
...