By definition, a Right triangle is a triangle that has an angle that measures 90 degrees (which also called "Right angle").
For this case, you can identify that the triangle given in the exercise is a Right triangle.
To find the measure of the missing angle, you need to use Arccosine function, which is the inverse of the cosine function:
[tex]\alpha=\cos ^{-1}(\frac{a}{h})[/tex]
Where "α (alpha)" is the angle you must find, "a" is the adjacent side and "h" is the hypotenuse.
You can set up that, for this case:
[tex]\begin{gathered} a=11 \\ h=23 \end{gathered}[/tex]
Then, substituting values and evaluating, you get that the measure of the angle is:
[tex]\begin{gathered} \alpha=\cos ^{-1}(\frac{11}{23}) \\ \alpha=61.42\degree \end{gathered}[/tex]
Rounding the answer to nearest whole degree, you get:
[tex]\alpha\approx61\degree[/tex]
The answer is: Option C.
