Calculate cartesian coordinates of geographical points

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I have 2 points expressed in (latitude,longitude) and I want to calculate the angle with respect to the north pole.

Since the two points are very near (like hundred of meters), is it possible to consider the two points in the cartesian system simply as:

x=longitude
y=latitude

Then, simply applying $\arctan(y/x)$, I get the angle from the equator.

Is this correct?