Russian Translation(s) & Details for 'hypotenuse'

English Word: hypotenuse

Key Russian Translations:

• гипотенуза [ɡʲɪpɐˈtʲenʊzə] - [Formal, Technical (used in mathematical and scientific contexts)]

Frequency: High (Common in educational, scientific, and mathematical discussions, especially in technical fields).

Difficulty: Intermediate (B1 level; requires basic understanding of Russian grammar and vocabulary, but familiarity with mathematical terms can ease learning for STEM students).

Pronunciation (Russian):

гипотенуза: [ɡʲɪpɐˈtʲenʊzə]

Note on гипотенуза: The stress falls on the third syllable ('te'), which is a common challenge for English speakers due to the palatalized 't' sound. Pronounce it with a soft 'g' at the beginning, similar to the 'y' in "yes".

Audio: []

Meanings and Usage:

The side opposite the right angle in a right-angled triangle.

Translation(s) & Context:

• гипотенуза - Used in formal mathematical contexts, such as geometry lessons or technical writing.

Usage Examples:

• В прямоугольном треугольнике гипотенуза является самой длинной стороной.

  In a right-angled triangle, the hypotenuse is the longest side.

• Чтобы найти длину гипотенузы, используйте теорему Пифагора.

  To find the length of the hypotenuse, use the Pythagorean theorem.

• Гипотенуза треугольника ABC равна 10 см.

  The hypotenuse of triangle ABC is 10 cm.

• В реальной жизни гипотенуза может представлять диагональ прямоугольника.

  In real life, the hypotenuse can represent the diagonal of a rectangle.

• Студенты изучают гипотенузу на уроках геометрии.

  Students study the hypotenuse in geometry lessons.

Russian Forms/Inflections:

"Гипотенуза" is a feminine noun in the second declension (second conjugation for nouns). It follows standard patterns for Russian feminine nouns ending in -а. Below is a table of its inflections based on case and number:

Note: This word does not have irregular forms, making it straightforward for learners once basic declension rules are understood.

Russian Synonyms/Antonyms:

• Synonyms:
  • диагональ (diaginal) - Used in contexts where the hypotenuse acts as a diagonal in a right-angled shape; slight nuance in broader geometric applications.
  • противоположная сторона (protivopolozhnaya storona) - A more descriptive term, often used in explanatory texts but less technical.
• Antonyms:
  • катет (cathetus) - Refers to the other sides of the right-angled triangle, providing contrast in geometric discussions.

Related Phrases:

• Длина гипотенузы - Length of the hypotenuse (used in calculations, e.g., in physics or engineering).
• Теорема о гипотенузе - Theorem about the hypotenuse (refers to Pythagorean theorem variants).
• Гипотенуза прямоугольного треугольника - Hypotenuse of a right-angled triangle (common in educational contexts).

Usage Notes:

"Гипотенуза" directly corresponds to the English "hypotenuse" and is primarily used in formal, academic, or technical settings. It is a loanword from Greek via Latin, so it retains a neutral, scientific tone. When choosing this term, ensure the context is mathematical; in everyday Russian, more descriptive phrases might be used. Grammatically, always treat it as a feminine noun and decline it according to the rules outlined above. For English learners, note that Russian mathematical vocabulary often integrates into sentences without articles, unlike English.

Common Errors:

• Error: Using the word in the wrong case, e.g., saying "длина гипотенуза" instead of "длина гипотенузы" (genitive case required after "длина").

  Correct: "Длина гипотенузы равна 5 см." (The length of the hypotenuse is 5 cm.)

  Explanation: Russian requires proper declension; forgetting this can make the sentence grammatically incorrect.

• Error: Confusing it with "катет" and using it interchangeably.

  Correct: Use "гипотенуза" only for the side opposite the right angle, not for the adjacent sides.

  Explanation: This mix-up stems from similar contexts in triangles; always verify the geometric position.

Cultural Notes:

As a mathematical term, "гипотенуза" doesn't carry significant cultural connotations in Russian culture, but it reflects Russia's strong emphasis on STEM education, influenced by historical figures like Nikolai Lobachevsky. In Russian-speaking regions, geometry is a core part of school curricula, making this term familiar from an early age and symbolizing the importance of logical reasoning in education.

Related Concepts:

• катет (cathetus)
• прямоугольный треугольник (right-angled triangle)
• теорема Пифагора (Pythagorean theorem)