Understanding the Right-Angled Triangle
In a right-angled triangle, the side opposite the right angle is referred to as the hypotenuse. This triangle has one angle equal to 90 degrees, which is the defining characteristic of a right-angled triangle.
Definition of Hypotenuse
- The hypotenuse is the longest side of the triangle.
- It is situated opposite the right angle, providing a critical reference for various geometric calculations.
Properties of the Hypotenuse
- Longest Side: In any right-angled triangle, the hypotenuse is always longer than either of the other two sides, known as the legs.
- Pythagorean Theorem: The relationship between the lengths of the sides of a right-angled triangle is expressed through the Pythagorean theorem: a² + b² = c², where c is the hypotenuse and a and b are the lengths of the other two sides.
Uses of the Hypotenuse
- Trigonometry: The hypotenuse is essential in trigonometric functions, such as sine, cosine, and tangent, which relate the angles of the triangle to the lengths of its sides.
- Real-World Applications: Understanding the hypotenuse is crucial in various fields, including architecture, engineering, and physics, where right-angled triangles frequently appear.
Conclusion
In summary, the hypotenuse is a fundamental concept in geometry, particularly within the context of right-angled triangles. Its properties and relationships with the other sides play a vital role in both theoretical and practical applications.

The side opposite to right angle is called hypotenuse.