How to calculate the altitude of the Moon?

With the known latitude coordinate of the observing position, how to find the altitude of the moon when it is high, i.e when it crosses the local meridian?

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May be this is out of your scope, but I saw those programs may help you. There is a cool software Digital planetarium application, free to download. And another one here but shareware Starry Night – Ahmed Hamdy Dec 17 '13 at 9:11
Thanks :) But, I'm looking for a mathematical approach as it was asked in one of my astronomy homeworks. – Karthikeyan KC Dec 17 '13 at 17:48
If it is homework, shouldn't you be attempting to research the answer yourself, or figure it out for yourself? The point being to help you comprehend what is going on, not just obtain an answer? – Jeremy Feb 18 '14 at 4:04
@Jeremy That is exactly what I did (sort of) :) AstroFloyd's answer did help me to comprehend the concept a bit, and later I got a clarified answer from my class. – Karthikeyan KC Feb 18 '14 at 13:12

The transit altitude of an object does not only depend on your latitude ($b$), but also on the declination of the object ($\delta$): $$h_\mathrm{tr} = \arcsin\left(\sin b \sin \delta + \cos b \cos\delta\right).$$