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Maths
3 Dec 2025
249
2 pages
Keira @keira_nuur
A comprehensive guide to understanding Pythagorean theorem in right-angled triangles and basic trigonometric functions.
The second page explores trigonometric ratios and their application in right-angled triangles. It focuses on the three main trigonometric functions sine, cosine, and tangent.
Vocabulary Key terms introduced include
Example The page demonstrates calculating angles using inverse trigonometric functions
Highlight The relationship between sides and angles is clearly illustrated through trigonometric ratios, showing how to find unknown angles when side lengths are known.
The first page introduces the fundamental concept of the Pythagorean theorem and its practical application in right-angled triangles. The theorem is expressed through the equation a² + b² = c², where c represents the hypotenuse and a and b represent the other two sides of the right triangle.
Definition The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (longest side) equals the sum of squares of the other two sides.
Example A right triangle with sides 2 and 4 has its hypotenuse calculated as follows 2² + 4² = c² 4 + 16 = c² c = √20 ≈ 4.47
Highlight Multiple worked examples demonstrate how to find missing sides using the theorem, including cases where the hypotenuse is known and one side needs to be calculated.
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
6
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the fundamentals of trigonometry with a focus on SOHCAHTOA. This summary covers how to label triangle sides, apply trigonometric formulas, and calculate missing angles using inverse functions. Ideal for GCSE Maths students looking to master right triangle calculations.
MathsExplore essential trigonometry concepts including the Law of Sines, Law of Cosines, and Pythagorean Theorem. This summary covers key formulas for right and non-right angle triangles, helping you determine missing sides and angles effectively. Ideal for exam preparation and quick revision.
MathsExplore the fundamentals of trigonometry with a focus on SOHCAHTOA. This study resource covers how to calculate missing angles in right-angled triangles using sine, cosine, and tangent ratios. Ideal for students looking to master trigonometric concepts and solve practical problems.
MathsExplore the fundamentals of trigonometry with a focus on right triangles. This study resource covers key concepts such as opposite and adjacent sides, trigonometric ratios, and practical examples for calculating angles and side lengths. Ideal for GCSE Maths students seeking to master trigonometric problems.
MathsExplore essential trigonometric concepts including hypotenuse, opposite, and adjacent sides, along with exact values for sine, cosine, and tangent at key angles (0°, 30°, 45°, 60°, 90°). This summary provides a clear understanding of trigonometric ratios and their applications.
MathsExplore the essential concepts of trigonometry, focusing on sine, cosine, and tangent functions in right-angled triangles. This summary covers the definitions of hypotenuse, opposite, and adjacent sides, along with practical applications for calculating unknown sides using trigonometric ratios. Ideal for students seeking a clear understanding of trigonometric principles.
MathsQuotes from every main character
English LiteratureApp 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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Keira
@keira_nuur
A comprehensive guide to understanding Pythagorean theorem in right-angled triangles and basic trigonometric functions.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The second page explores trigonometric ratios and their application in right-angled triangles. It focuses on the three main trigonometric functions: sine, cosine, and tangent.
Vocabulary: Key terms introduced include:
Example: The page demonstrates calculating angles using inverse trigonometric functions:
Highlight: The relationship between sides and angles is clearly illustrated through trigonometric ratios, showing how to find unknown angles when side lengths are known.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The first page introduces the fundamental concept of the Pythagorean theorem and its practical application in right-angled triangles. The theorem is expressed through the equation a² + b² = c², where c represents the hypotenuse and a and b represent the other two sides of the right triangle.
Definition: The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (longest side) equals the sum of squares of the other two sides.
Example: A right triangle with sides 2 and 4 has its hypotenuse calculated as follows: 2² + 4² = c² 4 + 16 = c² c = √20 ≈ 4.47
Highlight: Multiple worked examples demonstrate how to find missing sides using the theorem, including cases where the hypotenuse is known and one side needs to be calculated.
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
6
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the fundamentals of trigonometry with a focus on SOHCAHTOA. This summary covers how to label triangle sides, apply trigonometric formulas, and calculate missing angles using inverse functions. Ideal for GCSE Maths students looking to master right triangle calculations.
MathsExplore essential trigonometry concepts including the Law of Sines, Law of Cosines, and Pythagorean Theorem. This summary covers key formulas for right and non-right angle triangles, helping you determine missing sides and angles effectively. Ideal for exam preparation and quick revision.
MathsExplore the fundamentals of trigonometry with a focus on SOHCAHTOA. This study resource covers how to calculate missing angles in right-angled triangles using sine, cosine, and tangent ratios. Ideal for students looking to master trigonometric concepts and solve practical problems.
MathsExplore the fundamentals of trigonometry with a focus on right triangles. This study resource covers key concepts such as opposite and adjacent sides, trigonometric ratios, and practical examples for calculating angles and side lengths. Ideal for GCSE Maths students seeking to master trigonometric problems.
MathsExplore essential trigonometric concepts including hypotenuse, opposite, and adjacent sides, along with exact values for sine, cosine, and tangent at key angles (0°, 30°, 45°, 60°, 90°). This summary provides a clear understanding of trigonometric ratios and their applications.
MathsExplore the essential concepts of trigonometry, focusing on sine, cosine, and tangent functions in right-angled triangles. This summary covers the definitions of hypotenuse, opposite, and adjacent sides, along with practical applications for calculating unknown sides using trigonometric ratios. Ideal for students seeking a clear understanding of trigonometric principles.
MathsQuotes from every main character
English LiteratureApp 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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Sociology