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In a right-angled triangle the area of the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares of the other two sides.

Q: Can you state the Pythagorean Theorem not just the formula?

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the pythagorean theorem i would just like to say that he did not discover that, it was found in 800 B.C

There is a Pythagorean theorem that actually works for every triangle. Its just that for right triangles it can be simplified to A2+B2=C2 due to the properties of cosines. The law of cosines states that for a triangle with sides A, B, and C, and angles a, b, and c (with side C being opposite angle c), C2 = A2 + B2 - (2 x A x B x cos c). This formula will work for any triangle. Now imagine that we are talking about a right triangle, with side C the hypotenuse (just like in the classic Pythagorean theorem) and angle c the right angle. The cosine of a 90 degree angle is 0, which means that the part in bold would completely drop out of the equation, leaving us with A2+B2=C2 . The cosine of any other angle possible on a triangle would result in some other number, making A2+B2=C2 not work.

If the prism is a rectangular parallelepiped (that is, all the angles are right angles), just add the squares of the 3 dimensions (length, width, and height) together, and take the square root. This involves 2 applications of the Pythagorean Theorem.

The Pythagorean theorem can be done this way. a²+b²=c² lets say that you have a triangle with three sides, but you are only given two. Their values are 3 and 4. Now you have to fill in the values with a=3 and b=4 (doesn't matter which order you put it in) 3²+4²=c² c is still unknown so we have to do the next step. 3² is 9 and 4² is 16. knowing this, we have to do this next: 9+16=c² 9+16 is 25. 25=c² now you must get rid of the ². you do this by using the square root. don't ask me why you square root, that's just how the Pythagorean theorem works. √25=√c² the square root gets rid of the c squared so its just the square root of 25. 5=c triangle sides: 3,4,5 The process can also be reversed. a²=c²-b² or b²=c²-a² P.S: Please recommend using button below, thank you. James A. Garfield, the twentieth president of the United States, discovered an original proof of the Pythagorean theorem. The proof is algebraic in nature and uses the formula for the area of a trapezoid. See the link below for details. Garfield is credited with an original proof of this famous theorem. Many of the presidents undoubtedly proved it in geometry class after studying their books.

There is a famous theorem that you use to solve this problem, namely the Pythagorean theorem which says that the square on the hypotenuse is equal to the sum of the squares on the opposite sides. (The hypotenuse is the longest side; the other sides are commonly called legs.) If you know the hypotenuse and one leg you can find the other leg by simple algebra. Just subtract the square of the leg you know from the square of the hypotenuse and take the square root of this difference. Bingo! You have your answer.

Related questions

The square on the hypotenuse of a right-angled triangle is equivalent to the sum of the squares on the two adjacent sides.

If you drive 9 miles north from your house, then turn and drive 12 miles east, you can use the Pythagorean theorem to calculate that you wind up 15 miles from home. You don't need a graph at all to do that. You just have to know the Pythagorean theorem.

the pythagorean theorem i would just like to say that he did not discover that, it was found in 800 B.C

You use the Pythagorean Theorem: a2 + b2 = c2. Variables a and b are the shorter sides; c is the hypotenuse. Just plug the values for the sides into the Pythagorean Theorem and solve for the missing side.

The pythagorean theory or pythagorean theorem is a formula to find the leg or the hypotenuse for a right triangle. There are three parts to a triangle, The legs(A2) and (B2). The hypotenuse (C2). The hypotenuse is always the longest side of the triangle it is always adjacent to the 900 angle of the right triangle. The actual pythagorean theorem is A2 + B2 = C2. Example: A=2 B= 4 C=? A2 + B2 =C2 22 + 42 =C2 4 + 16= C2 20=C2 Now you find the square root for the two numbers you just added 4.4 = C

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: Using a protractor make a 90o AngleDraw 2 lines (Sides A & B) that make up the 90o Angle you measured out in Step 1Draw Side A - 5 cm in lengthDraw Side B - 8 cm in lengthDraw Side C - the Hypotenuse (A line that Connects Sides A and B) - But Do NOT Measure This with your ruler YET.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.52 + 82 = C2 (WHERE C2 is the Length of Side C/The Hypotenuse Squared)So Now we have the Equation: C2 = 25 + 64 = 89Now 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:C = 9.434 cmLAST 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.

Use Pythagorean theorem (a2 + b2 = c2). The diagonal measurement is just under 17.122 + 122 = c2144 + 144 = c2288 = c2c = SQRT288 = 16.9705627484771

The law of cosines with a right angle is just the pythagorean theorem. The cosine of 90 degrees is 0. That is why the hypotenuse squared is equal to the sum of both of the legs squared

There is a Pythagorean theorem that actually works for every triangle. Its just that for right triangles it can be simplified to A2+B2=C2 due to the properties of cosines. The law of cosines states that for a triangle with sides A, B, and C, and angles a, b, and c (with side C being opposite angle c), C2 = A2 + B2 - (2 x A x B x cos c). This formula will work for any triangle. Now imagine that we are talking about a right triangle, with side C the hypotenuse (just like in the classic Pythagorean theorem) and angle c the right angle. The cosine of a 90 degree angle is 0, which means that the part in bold would completely drop out of the equation, leaving us with A2+B2=C2 . The cosine of any other angle possible on a triangle would result in some other number, making A2+B2=C2 not work.

I don't think I could make the proof clear without a diagram, so you must check the related links to read it. I will say that it is algebraic in nature and is based on knowing how to find the area of a trapezoid. The first link is a student link and may not stay up for long. The second link contains several proofs of the Pythagorean theorem and you will have to hunt in it to find Garfield's proof, but it is there.

he created because he wanted to show that numbers have mystical and spirituals powers to the world he wanted to keep it a secret between him and just the brotherhood of Pyhtagorean's which are now called Pythagorean's Secret Society.

It's not as complicated as it sounds; okay. Picture a right triangle. It has three sides, or legs. One side is leg a, the other leg b, and the other leg c. The point of it is just to find what one of the leg's measurements are. The Pythagorean Theorem is technically just "a2 + b2 = c2"So it's saying that you multiply whatever leg a is by itself, and leg b by itself, add them together, and that will get you c2. Then use a calculator to find the square root of whatever total you got for c2.