The right-angled triangle and its terminology

What is a right-angled triangle?

A right-angled triangle has one right angle, that is, an angle of 90 degrees. It is the basic shape underpinning all of trigonometry: as soon as a triangle has a right angle, we can use the sine, cosine and tangent functions.

The three sides have specific names

In a right-angled triangle, each side has a specific name:

Side	Definition
Hypotenuse	The longest side, always opposite the right angle
Adjacent side	The side touching the angle under consideration (other than the right angle)
Opposite side	The side opposite the angle under consideration

Example

Let ABC be a right-angled triangle with the right angle at A. We are interested in angle B.

• BC is the hypotenuse (opposite the right angle at A)
• AB touches angle B -> this is the adjacent side
• AC faces angle B -> this is the opposite side

Common pitfall

The opposite side and the adjacent side change names depending on which angle you are looking at! If we were to examine angle C instead of B, then AC would become the adjacent side and AB the opposite side. Only the hypotenuse never changes: it always remains the side opposite the right angle.