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Formula

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Very Useful Video

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The above symbol is for square root. It will be useful when doing Pythagoras Theorem questions.

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Hypotenuse:
The longest side of the right angled triangle. It is usually side c in questions. This side is always opposite the right angle, like in the image below.

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The other two sides of the right angled triangle are known as the adjacent and the opposite.

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Look at the right angled triangle below. 5 squared, 25, + 12 squared, 144, = 169, which is 13 squared. 13cm is the longest side, known as the hypotenuse.

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Useful Link (BBC Bitesize)

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BBC Bitesize - KS3 Maths - Pythagoras' theorem - Revision 1

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Learn and revise Pythagoras' theorem with BBC Bitesize KS3 Maths to help you work out the length of any of the sides on a triangle.

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A self marking exercise on the application of Pythagoras' Theorem.

Here are some questions which can be answered using Pythagoras' Theorem. You can earn a trophy if you get at least 9 questions correct. Each time you finish a question click the 'Check' button lower down the page to see if you got it right!

Description of Levels

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Level 1 - Finding the hypotenuse

Level 2 - Finding a shorter side

Level 3 - Mixed questions

Level 4 - Pythagoras coordinates

Level 5 - Pythagoras' Theorem exercise

Level 6 - Pythagoras' Theorem harder exercise

Exam Style questions requiring an application of Pythagoras' Theorem and trigonometric ratios to find angles and lengths in right-angled triangles.

Three Dimensions - Three dimensional Pythagoras and trigonometry questions

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don't yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Curriculum Reference

Pythagoras' Theorem

The area of the square on the hypotenuse of a right angled triangle is equal to the sum of the areas of the squares on the two shorter sides.

You may have learned the theorem using letters to stand for the lengths of the sides. The corners (vertices) of the right-angled triangle is labelled with capital (upper case) letters. The lengths of the sides opposite them are labelled with the corresponding small (lower case) letters.

Alternatively the sides of the right-angled triangle may me named using the capital letters of the two points they span.

As triangle can be labelled in many different ways it is probably best to remember the theorem by momorising the first diagram above.

To find the longest side (hypotenuse) of a right-angled triangle you square the two shorter sides, add together the results and then find the square root of this total.

To find a shorter side of a right-angled triangle you subtract the square of the other shorter side from the square of the hypotenuse and then find the square root of the answer.

Example

AB ² = AC ² - BC ²
AB ² = 4.7 ² - 4.1 ²
AB ² = 22.09 - 16.81
AB ² = 5.28
AB = √5.28
AB = 2.3m (to one decimal place)

The diagrams aren't always the same way round. They could be rotated by any angle.

The right-angled triangles could be long and thin or short and not so thin.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.

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A self marking exercise on the application of Pythagoras' Theorem. Here are some questions which can be answered using Pythagoras' Theorem. You can earn a trophy if you get at least 9 questions correct. Each time you finish a question click the 'Check' button lower down the page to see if you got it right!

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Exam Style Questions

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Mini Test

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BBC - KS3 Bitesize Maths - Pythagoras theorem : Test

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Answers to exam style questions