What are the hypotenuse and legs?

Opposite side versus touching sides

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.

In a right triangle with legs 6 and 8, the side opposite the right angle is 10. Calling that side a leg would place the numbers into later formulas incorrectly. Start at the square corner every time, then name the side across from it hypotenuse.

The words legs and hypotenuse are structural labels, so they survive rotation of the drawing. A right triangle can point in any direction on the page and still have exactly two legs meeting at the right angle and one hypotenuse across from it.

• 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 these side names help

• 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.

Three side-naming checks

• 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.