Any time you measure distance using triangulation or utilise angles in theorems.
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The great pythagorean theorm: a(squared) + b(squared) = c(squared)
You would use the Pythagorean Theorem when you are trying to determine the length of a side on a right triangle.ORYou might use the Pythagorean Theorem if you are carpenter or builder. A carpenter might use the Pythagorean Theorem to find the length of the hypotenuse (longest side of the triangle) or the length of the wall or roof. Use can use this methed or theorem in any building situation.
It was years before, Pythagoras(580 BC - 500 BC) is said to have discovered Pythagorean Theorem. Strangely, 5 centuries after Pythagoras lived, the theorem Pythagorean was attributed to him. The discovery of the theorm Pythagorean came when Pythagoras was waiting for the tyrannical ruler, Polycrates. An interesting idea had flashed Pythagoras mind: A diagonal line can be used to cut or divide the square and two right triangles would be produced from the cut sides. After examining it further, Pythagoras formulated the idea in mind. Happy to help you.
Although the Pythagorean theorem (sums of square of a right angled triangle) is called a theorem it has many mathematical proofs (including the recent proof of Fermats last theorem which tangentially also prooves Pythagorean theorem). In fact Pythagorean theorem is an 'axiom', a kind of 'super law'. It doesn't matter if anyone does oppose it, it is one of the few fundamental truths of the universe.
Architects use the Pythagorean theorem to check distances, heights, etc...that cant be measured