A line makes an angle of $45^\circ$ with the $x$-axis and $60^\circ$ with the $y$-axis, and an acute angle with the $z$-axis. What is that angle?

Explanation

1. 01

   $\cos^{2} 45^\circ + \cos^{2} 60^\circ + \cos^{2} \gamma = 1$: $\frac{1}{2} + \frac{1}{4} + \cos^{2} \gamma = 1$.

2. 02

   $\cos^{2} \gamma = \frac{1}{4}$, and for an acute angle $\cos \gamma = \frac{1}{2}$: $\gamma = 60^\circ$.