What Is a Right Triangle?

What Is a Right Triangle?

A right triangle (or a right-angled triangle) is a triangle containing an angle of 90° (called a right angle).

Dictionary Definition

The Oxford English Dictionary defines a right triangle as "a triangle containing a right angle."

The Parts of a Right Triangle

  • A right triangle has one right angle (an angle of 90°). It is shown by drawing a small square.

  • The longest side (opposite the right angle) is called the hypotenuse.

  • The other two shorter sides are called legs or catheti (singular cathetus). They are perpendicular to each other.

  • If another angle is labelled (such as the angle labelled θ in the image below) then we can name the two shorter sides.

    The side next to the angle is called the adjacent. The side opposite the angle is called the opposite.

    Note: The adjacent and opposite only exist in relation to an angle. The same side can be an adjacent or an opposite depending on which angle they refer to.

The Uses of a Right Triangle

The right triangle is one of the most useful triangles in mathematics.

It is used for Pythagoras' theorem and in trigonometry.

The slider below gives more information about the uses of a right triangle.

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See Also

What is a triangle? What is Pythagoras' theorem? Learn more about Pythagoras' theory ( interactive widget) Learn more about the sine function in trigonometry ( interactive widget) Learn more about the cosine function in trigonometry ( interactive widget)