hypotenuse

Meanings

• noun

  The side of a right-angled triangle that is opposite the right angle, and is the longest side. It is the side that satisfies the Pythagorean theorem, a² + b² = c², where c represents the length of the hypotenuse.

  - "The length of the hypotenuse of a right triangle is 10 units."
  - "In a right triangle with legs of length 3 and 4 units, the length of the hypotenuse is 5 units."

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Variants

List of all variants of hypotenuse that leads to same result
hypotenuse , hypotenuses , hypothenuse , hypothenuses

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Etymology

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From the Greek word 'hypotenēs' meaning 'the lying beneath' or 'the under-poser'. This refers to the position of the side opposite the right angle in a right triangle.

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Trivia

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1. The hypotenuse is the side of a right triangle that always extends to the farthest point from the origin (0,0) in a Cartesian coordinate system.

2. The Pythagorean theorem was discovered around 500 BC, but it was not proven until 150 years later by the Greek mathematician Euclid.

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Related Concepts

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1. Pythagorean theorem: A fundamental theorem in geometry that relates the sides of a right triangle. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

2. Right triangle: A triangle with one right angle (an angle of exactly 90 degrees). The sides of a right triangle are referred to as the hypotenuse, the opposite side, and the adjacent side.

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Culture

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The hypotenuse is a fundamental concept in mathematics, particularly in geometry. It is used extensively in the study of right triangles and their properties.

How to Memorize "hypotenuse"

1. visualize
   

   - To visualize the hypotenuse, imagine a right triangle with legs of known length. Use a ruler or draw a line to represent the hypotenuse, which is the longest side that satisfies the Pythagorean theorem.

2. associate
   

   - Associate the word 'hypotenuse' with the concept of the longest side of a right triangle.

3. mnemonics
   

   - Use the mnemonic 'Help Out Remembering Triangles' (HORT) to remember the sides of a right triangle: Hypotenuse, Opposite, Right Angle, and Then Adjacent.

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