Pythagoras' theorem

Pythagoras' theorem relates the lengths of the sides of a right-angled triangle. This leaflet reminds you of the theorem and provides some revision examples and exercises.

Study the right-angled triangle shown.

In any right-angled triangle, ABC , the side opposite the right-angle is called the hypotenuse. Here we use the convention that the side opposite angle A is labelled a. The side opposite B is labelled b and the side opposite C is labelled c. Pythagoras' theorem states that the square of the hypotenuse, (c), is equal to the sum of the squares of the other two sides, (a + b )

Pythagoras' theorem: c = a + b

Example

Suppose AC = 9 cm and BC = 5 cm as shown. Find the length of the hypotenuse, AB .

Solution

Here, a = BC = 5, and b = AC = 9. Using the theorem

The hypotenuse has length 10.30cm.

Example

In triangle ABC shown, suppose that the length of the hypotenuse is 14cm and that a = BC = 3 cm. Find the length of AC.

Solution

Here a = BC = 3, and c = AB = 14. Using the theorem

The length of AC is 13.67cm.