The answer is: 12.30 degrees.
To solve this problem you must apply the proccedure shown below:
1. You run 22 meters horizontally and then you climb a rope vertically for 4.8 meters.
2. So. let's call the angle [tex]\alpha[/tex], therefore, you must find it using [tex]tan^{-1}[/tex], as following:
[tex]tan^{-1}(\alpha)=\frac{opposite}{adjacent} \\opposite=4.8\\adjacent=22[/tex]
3. Substitute values and solve for the angle:
[tex]tan^{-1}(\alpha)=\frac{4.8}{22}\\\alpha=12.30degrees[/tex]
