Detailed definition
Understanding Hypotenuse & Legs
Hypotenuse & Legs are the special side names used in a right triangle. In a right triangle, the hypotenuse is opposite the right angle and the other sides are the legs. The hypotenuse is the side opposite the right angle, while the legs are the two sides that meet at the right angle.
The hypotenuse is always the longest side because it lies opposite the largest angle in the triangle, namely the ninety-degree angle. That side naming is structural, not stylistic.
These names matter because many formulas depend on them. The Pythagorean Theorem, trigonometric ratios, and special-right-triangle patterns all assume that the triangle's sides have been identified correctly first.
Key facts
Important ideas to remember
- In a right triangle, the hypotenuse is opposite the right angle and the other sides are the legs.
- The hypotenuse is always opposite the right angle and is the longest side of the triangle.
- The legs are the two sides that form the right-angle corner.
- Correct side naming is required before using the Pythagorean Theorem or basic trigonometry.
Where it is used
Where hypotenuse & legs shows up
- Use these names when applying right-triangle formulas.
- Use them when identifying opposite, adjacent, and hypotenuse in trigonometry.
- Use them in construction and coordinate problems built around perpendicular sides.
Common mistakes
What to watch out for
- Do not call the longest side the hypotenuse unless it is opposite the right angle.
- Do not rename sides from the top or bottom of the page; the right-angle position controls the terminology.
- Do not mix leg names with opposite-adjacent labels, which depend on a chosen acute angle in trig contexts.