Pythagoras' theoremis one of the most useful tools in... Show more
Maths607 views·Updated May 23, 2026·2 pagesUnderstanding the Pythagorean Theorem
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Gabriela@gabriela_aowp
1
of 2
Finding the Hypotenuse and Shorter Sides
The Pythagoras theorem formula is your key to solving right-angled triangle problems. In this formula, represents the hypotenuse (the longest side opposite the right angle), whilst and are the two shorter sides.
When finding the hypotenuse, you simply add the squares of the two shorter sides. For example, with sides of 10cm and 20cm: $10^2 + 20^2 = 100 + 400 = 500\sqrt{500} = 22.4$ cm (to 3 significant figures).
For shorter sides, you'll need to rearrange the formula to . If you know the hypotenuse is 16cm and one side is 8cm, calculate: $16^2 - 8^2 = 256 - 64 = 192\sqrt{192} = 13.9$ cm (to 3SF).
Top Tip: Always check which side you're looking for - if it's the longest side, add the squares; if it's a shorter side, subtract them!
2
of 2
Complex Triangle Problems
Real-world problems often involve compound shapes where you need to apply Pythagoras' theorem multiple times. These problems might require you to find several missing lengths before reaching your final answer.
In the first example, you're working with a shape where you first find one missing side using $3.2^2 - 1.9^2 = 6.63\sqrt{6.63} = 2.572.1 + 2.57 = 4.67$ m for the total length BC.
The second problem shows a more complex shape where you need to identify right-angled triangles within the figure. Here, you calculate $10^2 - 6^2 = 64\sqrt{64} = 89^2 + 8^2 = 145\sqrt{145} = 12.0$ cm (to 3SF).
Remember: Break complex shapes into simple right-angled triangles, and always round your final answer to the required number of significant figures!
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Maths607 views·Updated May 23, 2026·2 pagesUnderstanding the Pythagorean Theorem
G
Gabriela@gabriela_aowp
Pythagoras' theorem is one of the most useful tools in maths for finding missing lengths in right-angled triangles. Whether you're calculating the hypotenuse or finding a shorter side, mastering this theorem will help you tackle geometry problems with confidence.
1
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Finding the Hypotenuse and Shorter Sides
The Pythagoras theorem formula is your key to solving right-angled triangle problems. In this formula, represents the hypotenuse (the longest side opposite the right angle), whilst and are the two shorter sides.
When finding the hypotenuse, you simply add the squares of the two shorter sides. For example, with sides of 10cm and 20cm: $10^2 + 20^2 = 100 + 400 = 500\sqrt{500} = 22.4$ cm (to 3 significant figures).
For shorter sides, you'll need to rearrange the formula to . If you know the hypotenuse is 16cm and one side is 8cm, calculate: $16^2 - 8^2 = 256 - 64 = 192\sqrt{192} = 13.9$ cm (to 3SF).
Top Tip: Always check which side you're looking for - if it's the longest side, add the squares; if it's a shorter side, subtract them!
2
of 2Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Complex Triangle Problems
Real-world problems often involve compound shapes where you need to apply Pythagoras' theorem multiple times. These problems might require you to find several missing lengths before reaching your final answer.
In the first example, you're working with a shape where you first find one missing side using $3.2^2 - 1.9^2 = 6.63\sqrt{6.63} = 2.572.1 + 2.57 = 4.67$ m for the total length BC.
The second problem shows a more complex shape where you need to identify right-angled triangles within the figure. Here, you calculate $10^2 - 6^2 = 64\sqrt{64} = 89^2 + 8^2 = 145\sqrt{145} = 12.0$ cm (to 3SF).
Remember: Break complex shapes into simple right-angled triangles, and always round your final answer to the required number of significant figures!
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Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5App Store
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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
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