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# What does Pythagoras' famous theorem involve?

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The Pythagorean theorem states that when a triangle has a right angle and all three sides are squared, the longest side squared will equal the size of the smaller two sides squared and summed. It is usually expressed as a^2+b^2=c^2.

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In the formula, the longest side is represented by the letter "c." This side is called the "hypotenuse." The other two sides are represented by "a" and "b."

A right angle is a 90-degree angle. A triangle with such an angle is called a right triangle. An example of the Pythagorean theorem in action is that if a right triangle has two sides which are 3 and 4 centimeters long, the hypotenuse will be 5 centimeters long. This is known because 3 squared is 9 and 4 squared is 16. When added together, the answer is 25. That is the size of the square of the hypotenuse, meaning if one finds the square root, one will obtain the length of the hypotenuse, in this case 5 centimeters.

The theorem is named after Pythagoras, a mathematician from ancient Greece. He is credited with creating the proof, although many argue that knowledge of the theorem predates Pythagoras. The theorem has numerous proofs.

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## Related Questions

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The formula z = sqrt (x^2 + y^2) is an equation for solving for one side of a right triangle if the other two sides are known. It is derived from the Pythagorean theorem, z^2 = x^2 + y^2, by taking the square root of both sides of the equation.

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Evaluating sin(arc-tan x) is a simple process that involves two steps: using a right-angled triangle to label the two sides and the angle in question, which is x, and using the Pythagoras theorem to calculate the remaining side and calculating the function from these values. Writing out the expression in words is the starting point of evaluating it. In this case, it is the sine of Arc-tan x.

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The basic trigonometric functions sine, cosine, and tangent give the ratio between two sides of a triangle with a given angle. The inverse trig functions find the angle if the ratio is known. Finding the inverse cosine often requires a calculator and more than five minutes if the side lengths are not given.