Subjects
Biology
Chemistry
AP Chemistry
English
AP English Literature
Maths
Dec 5, 2025
605
2 pages
Gabriela @gabriela_aowp
Pythagoras' theoremis one of the most useful tools in maths for finding missing lengths in right-angled triangles.... Show more
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 . Then take the square root 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 . Taking the square root gives you 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!
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 , giving m. Then you add this to another length 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 , so one section is cm. Then for the complete length AC, you use , giving 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!
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
7
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the principles of geometric similarity with a focus on triangular prisms. This study note covers key concepts such as scale factors, area and volume relationships, and includes solved exam-style questions to reinforce understanding. Ideal for GCSE students preparing for geometry assessments.
MathsThis comprehensive booklet provides essential practice and answers for students aiming for a Grade 5 in GCSE Maths. Covering key topics such as trigonometry, percentages, probability, and geometry, it includes worked examples and practice questions to enhance understanding and exam readiness.
MathsMaster the concept of enlargements in geometry with this detailed guide. Learn how to calculate positive, fractional, and negative scale factors, and accurately describe transformations including the center of enlargement. Ideal for students tackling geometry problems involving scaling and dilation.
MathsComprehensive solutions and explanations for past GCSE Maths Paper 1 questions. Topics include solving quadratics, area calculations, ratios, probability, and more. Ideal for students preparing for their exams, with clear step-by-step methods and key concepts highlighted.
MathsExplore essential trigonometric concepts including the Sine and Cosine rules, solving general triangles, and trigonometric equations. This study resource is tailored for GCSE Maths, Further Maths, and FSMQ students, providing clear examples and formulas to enhance understanding and problem-solving skills.
MathsPrepare for your GCSE Maths exam with this comprehensive non-calculator paper. This resource covers key concepts such as probability, ratios, area and perimeter, operations on fractions, and properties of exponents. Ideal for students looking to practice and improve their mathematical skills in a structured format. Includes a variety of question types to enhance understanding and exam readiness.
Maths323
3
App Store
Google Play
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.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
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.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
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.
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
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: . Then take the square root: 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: . Taking the square root gives you 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!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
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 , giving m. Then you add this to another length: 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 , so one section is cm. Then for the complete length AC, you use , giving 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!
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
7
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the principles of geometric similarity with a focus on triangular prisms. This study note covers key concepts such as scale factors, area and volume relationships, and includes solved exam-style questions to reinforce understanding. Ideal for GCSE students preparing for geometry assessments.
MathsThis comprehensive booklet provides essential practice and answers for students aiming for a Grade 5 in GCSE Maths. Covering key topics such as trigonometry, percentages, probability, and geometry, it includes worked examples and practice questions to enhance understanding and exam readiness.
MathsMaster the concept of enlargements in geometry with this detailed guide. Learn how to calculate positive, fractional, and negative scale factors, and accurately describe transformations including the center of enlargement. Ideal for students tackling geometry problems involving scaling and dilation.
MathsComprehensive solutions and explanations for past GCSE Maths Paper 1 questions. Topics include solving quadratics, area calculations, ratios, probability, and more. Ideal for students preparing for their exams, with clear step-by-step methods and key concepts highlighted.
MathsExplore essential trigonometric concepts including the Sine and Cosine rules, solving general triangles, and trigonometric equations. This study resource is tailored for GCSE Maths, Further Maths, and FSMQ students, providing clear examples and formulas to enhance understanding and problem-solving skills.
MathsPrepare for your GCSE Maths exam with this comprehensive non-calculator paper. This resource covers key concepts such as probability, ratios, area and perimeter, operations on fractions, and properties of exponents. Ideal for students looking to practice and improve their mathematical skills in a structured format. Includes a variety of question types to enhance understanding and exam readiness.
Maths323
3
App Store
Google Play
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.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
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.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
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