# Hypotenuse Worksheet • Section 1 of the The Hypotenuse worksheet contains 27 skills-based questions, in 3 groups to support differentiation
• Section 2 contains 3 applied The Hypotenuse questions with a mix of worded problems and deeper problem solving questions
• Section 3 contains 3 foundation and higher level GCSE exam style The Hypotenuse questions
• Answers and a mark scheme for all The Hypotenuse questions
• Follows variation theory with plenty of opportunities for students to work independently at their own level
• All questions created by fully qualified expert secondary maths teachers
• Suitable for GCSE maths revision for AQA, OCR and Edexcel exam boards

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### Hypotenuse at a glance

The hypotenuse is the name of the longest side of a right-angled triangle, it is the side that is opposite the right angle. It is one of the three sides of the triangle with the other two called the opposite and the adjacent.

Finding the hypotenuse of a triangle is a common exam question and is often asked as part of a word problem. In order to calculate the length of the hypotenuse when we know the other two sides we can use Pythagoras. The pythagorean theorem involves the lengths of the side of a right-angled triangle and states that the sum of the squares of the two shorter sides is equal to the square of the longest side (the square of the hypotenuse). In order to work out the missing length of the missing side we can square the lengths of the shorter sides, add them together and then square root the answer to work out the hypotenuse.

We can work out the length of an unknown side that is shorter than the hypotenuse by squaring the longest side and squaring the other shorter side, subtracting them and then square rooting the answer.

The side lengths of right-angled triangles can be decimals or integers. When they are whole numbers the three lengths are known as a pythagorean triple.

Looking forward, students can then progress to additional geometry worksheets, for example a 3D Pythagoras worksheet or . For more teaching and learning support on Geometry our GCSE maths lessons provide step by step support for all GCSE maths concepts.

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