Pythagoras' Theorem is one of the most useful tools in... Show more
Maths390 views·Updated May 27, 2026·2 pagesUnderstanding Pythagoras’ Theorem: Comprehensive GCSE Maths Guide
Em 👻@emken
1
of 2
Understanding Pythagoras' Theorem
Pythagoras' Theorem states that in any right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. Simply put: a² + b² = c², where c is always the hypotenuse (the longest side opposite the right angle).
You can rearrange this formula to find any side: c = √ or a = √. These variations come in handy depending on which side you need to calculate.
When finding the longest side (hypotenuse), start by labelling all sides clearly. Substitute the known values into the formula , then solve for c by taking the square root. For example, with sides of 6cm and 8cm, you'd calculate: c = √(6² + 8²) = √(36 + 64) = √100 = 10cm.
Pro Tip: Learn your square numbers (1², 2², 3², etc.) by heart as Pythagoras questions sometimes appear on non-calculator papers!
2
of 2
Finding the Shorter Sides
When you need to find a shorter side of a right-angled triangle, you'll use the rearranged formula b = √. This helps when you know the hypotenuse and one of the other sides.
Start by clearly labelling all sides, making sure c is the hypotenuse. For example, with a hypotenuse of 5cm and one side of 3cm, substitute these values: b = √(5² - 3²) = √(25 - 9) = √16 = 4cm.
Practice with different triangles to build your confidence. Whether you're finding a hypotenuse or a shorter side, the approach remains consistent: label, substitute, rearrange, and calculate. With some practice, you'll be solving these problems quickly and accurately.
Pro Tip: Look out for Pythagorean triples (3-4-5, 5-12-13, 8-15-17) that give whole number answers. Recognizing these patterns can save you calculation time!
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Maths390 views·Updated May 27, 2026·2 pagesUnderstanding Pythagoras’ Theorem: Comprehensive GCSE Maths Guide
Em 👻@emken
Pythagoras' Theorem is one of the most useful tools in geometry, helping you find unknown sides in right-angled triangles. This simple but powerful formula connects the three sides of a right-angled triangle and appears frequently in maths exams.
1
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Understanding Pythagoras' Theorem
Pythagoras' Theorem states that in any right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. Simply put: a² + b² = c², where c is always the hypotenuse (the longest side opposite the right angle).
You can rearrange this formula to find any side: c = √ or a = √. These variations come in handy depending on which side you need to calculate.
When finding the longest side (hypotenuse), start by labelling all sides clearly. Substitute the known values into the formula , then solve for c by taking the square root. For example, with sides of 6cm and 8cm, you'd calculate: c = √(6² + 8²) = √(36 + 64) = √100 = 10cm.
Pro Tip: Learn your square numbers (1², 2², 3², etc.) by heart as Pythagoras questions sometimes appear on non-calculator papers!
2
of 2Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Finding the Shorter Sides
When you need to find a shorter side of a right-angled triangle, you'll use the rearranged formula b = √. This helps when you know the hypotenuse and one of the other sides.
Start by clearly labelling all sides, making sure c is the hypotenuse. For example, with a hypotenuse of 5cm and one side of 3cm, substitute these values: b = √(5² - 3²) = √(25 - 9) = √16 = 4cm.
Practice with different triangles to build your confidence. Whether you're finding a hypotenuse or a shorter side, the approach remains consistent: label, substitute, rearrange, and calculate. With some practice, you'll be solving these problems quickly and accurately.
Pro Tip: Look out for Pythagorean triples (3-4-5, 5-12-13, 8-15-17) that give whole number answers. Recognizing these patterns can save you calculation time!
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