Calculating the hypotenuse

Pythagoras’ theorem allows us to calculate the length of any side of a right-angled triangle given the other two.

The square of the hypotenuse is equal to the sum of the squares of the remaining two sides.Pythagoras’ theorem

The hypotenuse is the longest side – it will always be opposite the right angle.

Three right-angled triangles with an arrow pointing to the hypotenuse

To represent this in a mathematical formula we can say;


Where \(a\) is the length of the hypotenuse and the other sides are labelled \(b\) and \(c\).

Right-angled triangle with sides a, b and c, where a is the hypotenuse

In this triangle we need to find the hypotenuse.

Right-angled triangle with sides of length 3cm, 4cm, and x, which is the hypotenuse

Pythagoras’ theorem tells us that:




To find \({x}\), we need to square root both sides added together.

\({x}\) = \(\sqrt{25}\)



Find the length AC, giving your answer to two decimal places.

Right-angled triangle where the side AB equals 6m, BC equals 2m, and AC is the hypotenuse

AC2 = 62 + 22

AC2 = 36 + 4

AC2 = 40

AC = \(\sqrt{40}\)

AC2 = 6.32455532

AC2 = 6.32 m (to two decimal places)