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Britain & the wider world: 1745 -1901
1l the quest for political stability: germany, 1871-1991
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Maths
7 Dec 2025
234
8 pages
Wiki :) @grav1ty.zer0
Right-angled triangles might seem tricky, but with the right tools, you'll be solving them like a pro! This... Show more
Pythagoras' theorem is brilliant for finding missing sides, but it can't help with angles. Trigonometry, on the other hand, is your go-to method when you need to find both missing sides and angles in right-angled triangles.
The Pythagoras formula is a² + b² = c², where c is always the longest side (hypotenuse). For example, if you have sides of 18m and 10m, the missing side equals √(18² - 10²) = √224 = 14.97m.
Quick Tip Always check which information you're given - if you have two sides and need the third, use Pythagoras. If you have angles involved, you'll need trigonometry!
SOHCAHTOA breaks down the three main trigonometric ratios Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, and Tan = Opposite/Adjacent. This simple memory trick will save you in every triangle problem.
When you know an angle and need to find a side, multiply the trigonometric ratio by the known side. For instance, if you have a 35° angle and a 12cm hypotenuse, the opposite side = sin(35°) × 12 = 6.9cm.
Practice identifying which sides are opposite, adjacent, and hypotenuse relative to your given angle. Once you've got this sorted, choosing the right ratio becomes straightforward.
Remember The hypotenuse is always the longest side, opposite the right angle. The opposite and adjacent sides change depending on which angle you're working with!
Converting between metres, centimetres, and millimetres follows a clear pattern that you can master quickly. Each step up or down the scale involves multiplying or dividing by 10 or 100.
From metres to centimetres, multiply by 100 . From metres to millimetres, multiply by 1000 . Going the other way, you divide by the same amounts.
The key is remembering the scale kilometres → metres (×1000) → centimetres (×100) → millimetres (×10). Once you've got this sequence down, you can convert between any units by combining the steps.
Pro Tip Write out the units in order when you're stuck - it helps you see how many steps you need to take and in which direction!
Area conversions work differently because you're dealing with squared units. When converting 7cm² to mm², you need to think about how many millimetres fit in each centimetre direction.
Since 1cm = 10mm, then 1cm² = 10mm × 10mm = 100mm². Therefore, 7cm² = 700mm². The same logic applies to larger conversions - 1m² = 10,000cm² because 100cm × 100cm = 10,000cm².
For volume conversions, you're working with cubes, so the multipliers get even bigger. Converting 2m³ to cm³ means 2 × (100 × 100 × 100) = 2,000,000cm³.
Memory Trick For area, square your conversion factor. For volume, cube it. So cm to mm (×10) becomes ×100 for area and ×1000 for volume!
Certain angles appear so frequently in trigonometry that memorising their values will speed up your calculations enormously. 30°, 45°, and 60° are the key angles you need to know by heart.
For 45° triangles, sin and cos both equal 1/√2, while tan equals 1. 30° and 60° angles are connected - what's sin for one becomes cos for the other. Sin(30°) = 1/2 and cos(30°) = √3/2.
These special triangles often appear in exam questions, and recognising them instantly gives you a massive advantage. You won't need to reach for your calculator every time.
Exam Hack If you see these angles in a question, there's usually a reason - the examiner expects you to use the exact values rather than decimal approximations!
You've now got all the tools needed to tackle any right-angled triangle problem. Pythagoras handles the pure side calculations, while SOHCAHTOA sorts out everything involving angles.
The secret to success is identifying what information you have and what you need to find. This determines whether you'll use sin, cos, tan, or Pythagoras' theorem.
Final Reminder Practice makes perfect with these techniques. The more triangles you solve, the quicker you'll 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
Quotes 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
Wiki :)
@grav1ty.zer0
Right-angled triangles might seem tricky, but with the right tools, you'll be solving them like a pro! This guide covers Pythagoras' theorem and trigonometry- two powerful methods that help you find missing sides and angles in triangles you'll encounter... Show more
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Improve your grades
Join milions of students
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Pythagoras' theorem is brilliant for finding missing sides, but it can't help with angles. Trigonometry, on the other hand, is your go-to method when you need to find both missing sides and angles in right-angled triangles.
The Pythagoras formula is a² + b² = c², where c is always the longest side (hypotenuse). For example, if you have sides of 18m and 10m, the missing side equals √(18² - 10²) = √224 = 14.97m.
Quick Tip: Always check which information you're given - if you have two sides and need the third, use Pythagoras. If you have angles involved, you'll need trigonometry!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
SOHCAHTOA breaks down the three main trigonometric ratios: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, and Tan = Opposite/Adjacent. This simple memory trick will save you in every triangle problem.
When you know an angle and need to find a side, multiply the trigonometric ratio by the known side. For instance, if you have a 35° angle and a 12cm hypotenuse, the opposite side = sin(35°) × 12 = 6.9cm.
Practice identifying which sides are opposite, adjacent, and hypotenuse relative to your given angle. Once you've got this sorted, choosing the right ratio becomes straightforward.
Remember: The hypotenuse is always the longest side, opposite the right angle. The opposite and adjacent sides change depending on which angle you're working with!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Converting between metres, centimetres, and millimetres follows a clear pattern that you can master quickly. Each step up or down the scale involves multiplying or dividing by 10 or 100.
From metres to centimetres, multiply by 100 . From metres to millimetres, multiply by 1000 . Going the other way, you divide by the same amounts.
The key is remembering the scale: kilometres → metres (×1000) → centimetres (×100) → millimetres (×10). Once you've got this sequence down, you can convert between any units by combining the steps.
Pro Tip: Write out the units in order when you're stuck - it helps you see how many steps you need to take and in which direction!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Area conversions work differently because you're dealing with squared units. When converting 7cm² to mm², you need to think about how many millimetres fit in each centimetre direction.
Since 1cm = 10mm, then 1cm² = 10mm × 10mm = 100mm². Therefore, 7cm² = 700mm². The same logic applies to larger conversions - 1m² = 10,000cm² because 100cm × 100cm = 10,000cm².
For volume conversions, you're working with cubes, so the multipliers get even bigger. Converting 2m³ to cm³ means 2 × (100 × 100 × 100) = 2,000,000cm³.
Memory Trick: For area, square your conversion factor. For volume, cube it. So cm to mm (×10) becomes ×100 for area and ×1000 for volume!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Certain angles appear so frequently in trigonometry that memorising their values will speed up your calculations enormously. 30°, 45°, and 60° are the key angles you need to know by heart.
For 45° triangles, sin and cos both equal 1/√2, while tan equals 1. 30° and 60° angles are connected - what's sin for one becomes cos for the other. Sin(30°) = 1/2 and cos(30°) = √3/2.
These special triangles often appear in exam questions, and recognising them instantly gives you a massive advantage. You won't need to reach for your calculator every time.
Exam Hack: If you see these angles in a question, there's usually a reason - the examiner expects you to use the exact values rather than decimal approximations!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
You've now got all the tools needed to tackle any right-angled triangle problem. Pythagoras handles the pure side calculations, while SOHCAHTOA sorts out everything involving angles.
The secret to success is identifying what information you have and what you need to find. This determines whether you'll use sin, cos, tan, or Pythagoras' theorem.
Final Reminder: Practice makes perfect with these techniques. The more triangles you solve, the quicker you'll spot which method to use!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
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
Quotes 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