right-angled triangle
Definition
- Noun:
- A triangle with one right angle: A right-angled triangle is a three-sided polygon (triangle) that contains one interior angle measuring exactly 90 degrees (a right angle). The side opposite this right angle is called the hypotenuse, and it is the longest side of the triangle.
Usage
- The term "right-angled triangle" is used in geometry to classify and describe a specific type of triangle based on its angles.
- It is commonly used in mathematical problems, proofs, and real-world applications involving measurements and calculations, such as in construction or navigation.
Examples
- Noun:
- To solve this problem, you first need to identify the right-angled triangle in the diagram.
- The Pythagorean theorem applies only to a right-angled triangle.
- A common example of a right-angled triangle is a set square used in technical drawing.
Advanced Usage
- "properties of a right-angled triangle": Refers to the geometric characteristics unique to this shape, such as the relationship between its sides defined by the Pythagorean theorem (a² + b² = c², where c is the hypotenuse).
- "solve a right-angled triangle": A mathematical process of finding the lengths of unknown sides or measures of unknown angles when some values are given.
Variants and Related Words
- Right triangle (n): A common synonym for "right-angled triangle," primarily used in American English.
- Hypotenuse (n): The longest side of a right-angled triangle, opposite the right angle.
- Legs (n): The two sides of a right-angled triangle that form the right angle.
Synonyms
- Right triangle: A triangle with a right angle.
Related Phrases and Concepts
- Pythagorean theorem: The fundamental relation in Euclidean geometry among the three sides of a right-angled triangle.
- Trigonometric ratios (sine, cosine, tangent): Ratios of side lengths in a right-angled triangle, used to define functions for any angle.
Noun
-
a triangle with one right angle
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