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Hypotenuse - GCSE Maths Definition

Reviewed by: Mark Curtis

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What is the hypotenuse?

In GCSE maths, the hypotenuse is the name given to the longest side of a right-angled triangle. It is the side opposite the right angle.

It is important to know which length is the hypotenuse when using Pythagoras’ theorem (it is the length ‘c’ in the formula a2 + b2 = c2).

Right-angled triangle with sides labelled a, b, and hypotenuse c. It includes a right-angle symbol at the intersection of sides a and b.
The hypotenuse is the length ‘c’ shown.

Knowing which length is the hypotenuse is also necessary when using trigonometry (sin, cos and tan). The names of the two shorter sides are the ‘opposite’ side and the ‘adjacent’ side, depending on where the angle is.

Two right-angled triangles, each labelled with sides: opposite (O), adjacent (A), hypotenuse (H), and angles labelled with theta (θ).
H is the hypotenuse, O is the opposite, A is the adjacent and 𝜃 is the angle

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Mark Curtis

Reviewer: Mark Curtis

Expertise: Maths Content Creator

Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.

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