The triangle concerned MUST be a right-angle triangle. If one of the angles is not 90 degrees, you cannot use the Pythagorean theorem!
Also, it must be remembered that the theorem only involves the magnitudes (lengths of the sides), you can't use it on i-j-k vectors or the like, only their magnitudes. As a result, it cannot tell us anything about the directions or angles between lines.
Other than that, the Pythagorean theorem is incredibly sound!
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Pythagorean theorem
With any right angle triangle
You can use pythagorean theorem twice to find the diagonal of a cube
pythagorean theorem was named from a greek mathemition called pythagorus (I think that's how you spell it)
The difference in the distance formula and the pythagorean theorem is that the distance formula finds the distance between two points while the pythagorean theorem usually finds the hypotenuse of a right triangle.