Latitude calculation using Day duration

I am currently studying for my exam in advanced photovoltaics. There is a question in a previous exam that states the following: Consider the day duration to be 10.8 hours, the tilt angle to be 30 degrees, and the declination angle to be 5.20 degrees. Calculate the latitude of this place. My approach was as follows: since I have the day duration, I have first calculated the hour angle at sunset = pi/12 * day duartion/2 = pi/12 * 10.8/2 = 9/20 pi radians, then I have used the hour angle at sunset formula as cos^-1 [-tan(declination angle)tan(latitude-tilt angle )] –> 9/20pi = os^-1 [-tan(13/40*pi)tan(latitude-1/6pi )], so now this is one equation in one unknown ( latitude ) and therefore solving for this unknown to find that the latitude is -29.7 degrees meaning that the location is approximately at latitude 30 degrees in the southern hemisphere. Is that right?