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Hypotenuse

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.

cc does not need to be the hypotenuse

legacy geogebra formula

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

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

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

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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