How to justify the reasonableness of these results?

"Derived" and "theoretical" mean the same thing, so you need to figure out what you are presenting here. Then what you want is "error calculation", which is figured from the uncertainty of your measurements. For example, if you measured the angle with a plastic protractor, that is certain within one degree. The value of g that you used is probably uncertain in the third decimal. So these errors would combine to give you a possible high figure and a possible low figure. These are called "error bars" when plotted on a graph.