If you are in Binghamton at the moment, 7:49 pm, 10/14 Polaris is at 41 degrees 57 minutes 21 seconds. I have 42 degrees 5 minutes as the north latiude of Binghamton. If you can move to 42 degrees 4 minutes, you will have an altitude for Polaris of almost exactly 42 degrees. Yes, Polaris does move a little; it is not perfectly in line with the earth's pole.
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43 degrees
The altitude of the celestial pole from the horizon actually tells you your latitude. So If I locate Polaris, the star that our earth's celestial pole points to and I see it's 40 degrees above the horizon to the north, I know that my latitude is 40 degrees north. Think about the extremes, if your on the equator looking for the celestial pole, you would see it on the northern horizon correct? (0 degrees) Now think of where the celestial pole would be pointing when on the north pole. You guessed it, straight up! (90 degrees)
Your at the equator if you see Polaris at the horizon
Equator
Due to the vast distance between the earth and polaris, the earths axis of rotation essentially lines up with polaris at all times, so when the stars are visible, and viewed from the north pole, the earths rotation causes the stars to appear to rotate around polaris.