Do you know Pythagoras Theorem had been put in to practice long before it was derived?

Answer 1

Of course. Something had to exist to be studied before a theory of explanation could be worked out and tested. That is the way that science works most of the time. The 3-4-5 right triangle for constructing right angles for construction had been around for millenia.

Answer 2

Yes, the theorem was used in conjunction with water wells across great expanses of territory to determine the curvature of the earth.

Measuring where the sunlight hit in the well from the top of the well at particular times of the day and using geometry, earlier scientists were able to determine curvature of the earth.

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Answer 3

Yes, Vedic Indians or Aryans have used it, Babylonians have used it. Aryan's used to prepare their sacrificial altars and tubs based on pythogorean formula.

Also, there is a school of thought, which believes Aryans learnt it from Babylonian mathematicians. But there are counter arguments against such theories.