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Maths
11 Dec 2025
254
3 pages
Sehar @ehar_oxdaozxefuetcct
SOHCAHTOA and Pythagoras' theorem are your best mates for solving right-angled triangles. Whether you need to find missing... Show more
SOHCAHTOA is a memory trick that breaks down into three key ratios. Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, and Tan = Opposite/Adjacent. The hypotenuse is always the longest side, opposite the 90° angle.
Before diving into calculations, identify what you've got and what you need. If you have an angle and the opposite side but need the hypotenuse, you'll use sine. For example, if sin(35°) = 20/H, then H = 20 ÷ sin(35°) = 34.9cm.
When you need to find an angle instead of a side, use the inverse functions (sin⁻¹, cos⁻¹, tan⁻¹). If cos(x) = 16/24, then x = cos⁻¹(16/24) = 48.2°.
Top Tip Always check which sides you can identify relative to your angle - this determines which ratio to use.
Real-world problems often require multiple steps and careful angle identification. When finding angle BAD in a complex shape, break it down into simpler right-angled triangles first.
Sometimes you'll need Pythagoras' theorem before using SOHCAHTOA. If you've got two sides of a right triangle, Pythagoras finds the third. Then use trigonometry for the angles.
For tricky problems, work systematically. Find missing sides using Pythagoras first, then tackle the angles. Remember that angles in complex shapes might need adding or subtracting from each other.
Remember When you see 25° and need angle BAD, you might need to add 90° + 7.6° = 97.6° depending on the triangle's orientation.
Pythagoras' theorem is brilliant for finding any side of a right-angled triangle when you know the other two. The hypotenuse (longest side) is always c in the formula c² = a² + b².
For complex problems involving multiple triangles, work step by step. Calculate intermediate lengths first, then use these to find your final answer. When finding diagonal AC in a rectangle, simply treat it as the hypotenuse of a right triangle.
Always give answers to the significant figures or decimal places asked for. Whether it's 1 d.p., 3 sig. fig., or exact values, check your calculator work and round appropriately.
Pro Strategy Draw clear diagrams and label everything you know - it prevents silly mistakes and helps you spot which method to use.
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.
2
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Comprehensive GCSE Maths resource on the Pythagorean Theorem. Learn the formula, step-by-step problem-solving techniques, and practice with example questions. Ideal for mastering right triangle calculations and understanding side lengths.
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.
MathsExplore 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.
MathsApp 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
Sehar
@ehar_oxdaozxefuetcct
SOHCAHTOA and Pythagoras' theorem are your best mates for solving right-angled triangles. Whether you need to find missing sides or angles, these tools will sort you out every time.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
SOHCAHTOA is a memory trick that breaks down into three key ratios. Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, and Tan = Opposite/Adjacent. The hypotenuse is always the longest side, opposite the 90° angle.
Before diving into calculations, identify what you've got and what you need. If you have an angle and the opposite side but need the hypotenuse, you'll use sine. For example, if sin(35°) = 20/H, then H = 20 ÷ sin(35°) = 34.9cm.
When you need to find an angle instead of a side, use the inverse functions (sin⁻¹, cos⁻¹, tan⁻¹). If cos(x) = 16/24, then x = cos⁻¹(16/24) = 48.2°.
Top Tip: Always check which sides you can identify relative to your angle - this determines which ratio to use.
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 require multiple steps and careful angle identification. When finding angle BAD in a complex shape, break it down into simpler right-angled triangles first.
Sometimes you'll need Pythagoras' theorem before using SOHCAHTOA. If you've got two sides of a right triangle, Pythagoras finds the third. Then use trigonometry for the angles.
For tricky problems, work systematically. Find missing sides using Pythagoras first, then tackle the angles. Remember that angles in complex shapes might need adding or subtracting from each other.
Remember: When you see 25° and need angle BAD, you might need to add 90° + 7.6° = 97.6° depending on the triangle's orientation.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Pythagoras' theorem is brilliant for finding any side of a right-angled triangle when you know the other two. The hypotenuse (longest side) is always c in the formula c² = a² + b².
For complex problems involving multiple triangles, work step by step. Calculate intermediate lengths first, then use these to find your final answer. When finding diagonal AC in a rectangle, simply treat it as the hypotenuse of a right triangle.
Always give answers to the significant figures or decimal places asked for. Whether it's 1 d.p., 3 sig. fig., or exact values, check your calculator work and round appropriately.
Pro Strategy: Draw clear diagrams and label everything you know - it prevents silly mistakes and helps you spot which method to use.
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.
2
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Comprehensive GCSE Maths resource on the Pythagorean Theorem. Learn the formula, step-by-step problem-solving techniques, and practice with example questions. Ideal for mastering right triangle calculations and understanding side lengths.
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.
MathsExplore 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.
MathsApp 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