Question: What name is given to the longest side in a right-angled triangle?

## Show answer

Hypotenuse.

In a right-angled triangle, the longest side is called the hypotenuse. This side is always opposite the right angle and is a crucial element in many mathematical calculations and theories, particularly in trigonometry and geometry.

The concept of the hypotenuse is most famously associated with the Pythagorean theorem, a fundamental principle in geometry attributed to the ancient Greek mathematician Pythagoras. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

This equation allows for the calculation of the length of the hypotenuse if the lengths of the other two sides are known, and vice versa. The Pythagorean theorem has widespread applications, not only in geometry but also in various fields such as physics, engineering, computer science, and even art.

Understanding the hypotenuse and its properties is essential for solving various mathematical problems, from simple triangle measurements to complex equations involving right-angled triangles.

The concept of the hypotenuse also extends beyond theoretical mathematics. It is used in practical applications such as navigation, construction, and physics. For example, in navigation, calculating the shortest path between two points often involves determining the hypotenuse of a right-angled triangle. In construction, ensuring structures are correctly aligned often requires the use of the Pythagorean theorem to verify right angles and lengths.