Can the Pythagoras theorem be proven emperically?

Answer 1

ANSWERYes The Pythagorean Theorem Can Be Proven Empirically.HOW?First, Lets Define The Theorem:In simplest terms, the Pythagorean Theorem is essentially a Formula that is TRUE for ANY/ALL RIGHT TRIANGLES (ANY Triangle that has ONE 90o ANGLE). The formula States: A2 + B2 = C2 , WHERE C is Always The Longest Side (Called The Hypotenuse) and is Always OPPOSITE the 90o Angle. A and B are The Other two sides of the triangle (not the Hypotenuse), the sides adjacent to the 90o Angle. To Prove The Pythagorean Theorem Empirically:First off lets define Empirically; all that it means, in this instance, is Show or Prove that the Theorem works through experience/experiment. This is very easy, just do the following:

1. Using a protractor make a 90o Angle
2. Draw 2 lines (Sides A & B) that make up the 90o Angle you measured out in Step 1
3. Draw Side A - 5 cm in length
4. Draw Side B - 8 cm in length
5. Draw Side C - the Hypotenuse (A line that Connects Sides A and B) - But Do NOT Measure This with your ruler YET.
6. Now since we need to PROVE that the Theorem is Correct, We have to Plug the length of the Sides A and B into the Theorem's Formula.
7. 52 + 82 = C2 (WHERE C2 is the Length of Side C/The Hypotenuse Squared)
8. So Now we have the Equation: C2 = 25 + 64 = 89
9. Now we need to Find what C equals, we do this by taking the Square Root of 89, and Since we know C is a Positive Number (Since its the Length of Side C), we can ignore the Negative portion of the Square Root and So We Know:
10. C = 9.434 cm
11. LAST STEP, NOW You MEASURE - with your Ruler, the Hypotenuse (Side C), and you will see that it equals 9.434 cm; therefore we have just Proved Empirically that the Pythagorean Theorem is Correct.