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Hypotenuse

The hypotenuse is the longest of the three sides of a right triangle.

It is always the side opposite the right angle.

The other two sides are called the catheti.

Hypotenuse

c does not need to be the hypotenuse

Side c is the hypotenuse only if it lies opposite the right angle.

However, if, for example, side a is opposite the right angle, then a is the hypotenuse (green side in the picture).

If b is opposite the right angle, then b is the hypotenuse.

legacy geogebra formula

Hypotenuse in a non-rectangular triangle?

If there is no right angle in a triangle, there is neither a hypotenuse nor catheti in it. The two terms are only used for right-angled triangles.

Calculating the length of the hypotenuse

If you want to calculate the length of the hypotenuse, then you may use

  • the Pythagorean theorem if the other two catheti are given, or

  • Sine or cosine if a cathetus and another angle are given.

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