•

27 Dec 2025

•

8 pages

GCSE Maths 2023 Revision Guide: Part 2

Wiki :)

@grav1ty.zer0

Right-angled triangles might seem tricky, but with the right tools,... Show more

1 / 8

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

Pythagoras vs Trigonometry - When to Use Each

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!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

SOHCAHTOA - Your Trigonometry Lifeline

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!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

Unit Conversions Made Simple

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 $7m = 700cm$ . From metres to millimetres, multiply by 1000 $13m = 13,000mm$ . 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!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

Area Conversions - Think in Squares

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!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

Special Angles - The Magic Numbers

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!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

Putting It All Together

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!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

We thought you’d never ask...

What is the Knowunity AI companion?

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.

Where can I download the Knowunity app?

You can download the app from Google Play Store and Apple App Store.

Is Knowunity really free of charge?

That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.

Most popular content: Trigonometric Ratios

Trigonometric Functions Overview

Explore the fundamentals of trigonometry, including the tangent, sine, and cosine functions. This summary covers key concepts such as SOH CAH TOA, trigonometric ratios, and methods for finding angles and sides in right triangles. Ideal for students preparing for exams or needing a quick reference.

Maths

Trigonometric Ratios Explained

Explore 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.

Maths

Trigonometry Fundamentals

Explore the essential concepts of trigonometry, focusing on right angle triangles. This summary covers key terms such as sine, cosine, and tangent, along with their relationships to opposite, adjacent, and hypotenuse sides. Ideal for Edexcel higher maths GCSE students preparing for exams.

Maths

Trigonometric Ratios Explained

Explore the fundamentals of trigonometry with a focus on the key concepts of hypotenuse, opposite, and adjacent sides. This summary covers essential formulas including sine, cosine, and tangent, along with step-by-step instructions for solving problems using SOH CAH TOA. Perfect for students looking to master trigonometric calculations.

Maths

Trigonometry & Area Formulas

Explore essential formulas for calculating the area of various shapes including rectangles, triangles, trapeziums, and circles. Additionally, understand trigonometric ratios (sin, cos, tan) and their exact values for special angles. This summary is perfect for quick revision and exam preparation.

Maths

Trigonometric Ratios Explained

Explore 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.

Maths

Trigonometric Ratios Explained

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.

Maths

Understanding Bearings and Trigonometry

Explore the fundamentals of bearings, including angle measurement and relationships in geometry. This study note covers key concepts such as trigonometric ratios, right triangles, and practical applications through example problems. Ideal for students looking to master bearings and their connection to trigonometry.

Maths

Trigonometric Ratios Explained

Explore the fundamentals of trigonometry with a focus on right triangles. This summary covers key concepts such as the definitions of opposite, adjacent, and hypotenuse sides, along with the SOH-CAH-TOA method for calculating trigonometric ratios. Ideal for students looking to master trigonometric equations and applications.

Maths

Most popular content in Maths

Comprehensive Maths Concepts

Explore essential mathematical concepts including powers, geometry, statistics, and probability. This resource features 65 pages of detailed explanations, diagrams, and examples to enhance your understanding of topics such as right triangles, volume calculations, and data representation. Ideal for students seeking to strengthen their numeracy skills and grasp complex mathematical principles.

Maths

GCSE maths notes

Pearson Edexcel

Maths

GCSE Higher Maths Essentials

Master key concepts in GCSE Higher Maths with this comprehensive summary covering geometry, algebra, probability, and circle theorems. Perfect for exam preparation, this resource includes essential formulas, angle facts, area calculations, and statistical measures to boost your understanding and performance. Ideal for students aiming for top grades.

Maths

Pythagoras theorem - foundation maths

Maths

Year 8 Math Concepts

Explore essential Year 8 math concepts including sequences, indices, area calculations, probability, and data representation. This knowledge organizer covers key topics such as central tendency, geometric properties, and algebraic manipulation, providing a comprehensive overview for effective study and understanding. Ideal for students preparing for assessments and seeking to strengthen their math skills.

Maths

Comprehensive Maths Concepts

Explore essential mathematical concepts including polynomial theorems, logarithmic properties, trigonometric functions, and integration techniques. This resource covers everything from solving inequalities to understanding exponential functions, providing a solid foundation for A-level mathematics. Ideal for students aiming for top grades.

Maths

Comprehensive Pure Mathematics

Explore detailed notes on Pure Mathematics Year 1, covering essential topics such as simultaneous equations, differentiation, integration, trigonometric functions, and more. Perfect for A Level Edexcel students seeking a thorough understanding of mathematical concepts and techniques.

Maths

Comprehensive Maths Concepts

Explore essential higher mathematics concepts including calculus, trigonometry, polynomials, and vector analysis. This summary covers key topics such as differentiation, integration, quadratic equations, and the properties of circles, providing a solid foundation for exam preparation. Ideal for students seeking a concise yet thorough review of advanced mathematical principles.

Maths

GCSE Maths (Higher) // Revision Guide

The only GCSE maths (higher) revision guide you need to get a grade 9! Contains every topic, each with all potential question types and their solutions.

Maths

Most popular content

An Inspector Calls: Character Insights

Explore in-depth analysis and key quotes for characters in J.B. Priestley's 'An Inspector Calls'. This resource covers Gerald Croft, Inspector Goole, Sheila Birling, Mrs. Birling, Eric Birling, and Eva Smith, focusing on themes of class, gender roles, and social responsibility. Ideal for students aiming for Grade 8 and above.

English Literature

aqa higher tier combined science - biology b1 : cell biology, paper 1

b1: cell biology - paper 1

Biology

Sociology of Families: Comprehensive Revision

Dive into an extensive overview of family dynamics, perspectives, and patterns in sociology. This resource covers key concepts such as family diversity, gender roles, marriage, and the impact of social policies on family structures. Perfect for A-Level Sociology students preparing for Paper 2.

Sociology

Comprehensive Crime & Deviance Overview

Explore an extensive revision of crime and deviance topics, including theories, types of crime, and the impact of media. This resource covers key concepts such as Marxism, functionalism, gender and crime, and the influence of globalization on criminal behavior. Ideal for students seeking a thorough understanding of criminology and its various theories. Type: Full Topic Revision.

Sociology

Sociology of Education Overview

Explore comprehensive A-Level Sociology notes on the education system, covering key theories, policies, and sociological perspectives. This resource includes insights on marketisation, gender roles, cultural deprivation, and educational inequalities, providing a thorough understanding of how education shapes social stratification and individual achievement. Ideal for exam preparation and in-depth study.

Sociology

Criminal Justice Evidence Rules

Explore the essential rules governing the use of evidence in criminal cases, including reliability, admissibility, and relevance. This summary covers key concepts such as the roles of personnel in investigations, the impact of witness testimonies, and the implications of plea bargaining. Ideal for Year 13 criminology students preparing for assessments.

Criminology

Biology Paper 1 Overview

Comprehensive study notes covering key concepts in cellular biology, human digestion, respiration, photosynthesis, and the circulatory system. This resource includes detailed explanations of cell structures, enzyme functions, nutrient absorption, and the impact of environmental factors on biological processes. Ideal for students preparing for Biology Paper 1 exams.

Biology

Macbeth: Guilt and Ambition

Explore the complex themes of guilt and ambition in Shakespeare's 'Macbeth'. This analysis covers key characters, including Macbeth and Lady Macbeth, their moral dilemmas, and the tragic consequences of their ambition. Ideal for students studying character motivations, thematic elements, and the psychological impact of power. Includes insights on the natural order, manipulation, and the descent into madness.

English Literature

Language Paper 1 Strategies

Master the AQA English Language Paper 1 with this comprehensive guide. Explore key strategies for language and structural analysis, critical evaluation, and creative writing. Learn how to effectively analyze texts, utilize literary techniques, and enhance your writing skills to excel in your exams.

English Language

Can't find what you're looking for? Explore other subjects.

Students love us — and so will you.

4.9/5

App Store

4.8/5

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

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Basil

Android user

David K

iOS user

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

Rohan U

Android user

Xander S

iOS user

Elisha

iOS user

Paul T

iOS user

Maths

•

237

•

27 Dec 2025

•

8 pages

GCSE Maths 2023 Revision Guide: Part 2

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

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Pythagoras vs Trigonometry - When to Use Each

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!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

SOHCAHTOA - Your Trigonometry Lifeline

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!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Unit Conversions Made Simple

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 $7m = 700cm$ . From metres to millimetres, multiply by 1000 $13m = 13,000mm$ . Going the other way, you divide by the same amounts.

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!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Area Conversions - Think in Squares

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!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Special Angles - The Magic Numbers

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.

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!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Putting It All Together

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!

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

$Pythagonis + trigonometry -only to find missing sides on P - Trig can find angles and sides. 5cm 7cm 7 trig Pythagorus $18^2-10^2$ $=\s$

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

We thought you’d never ask...

What is the Knowunity AI companion?

Where can I download the Knowunity app?

You can download the app from Google Play Store and Apple App Store.

Is Knowunity really free of charge?

That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.

Smart Tools NEW

Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines

Mock Exam

Quiz

Flashcards

Essay

Can't find what you're looking for? Explore other subjects.

Students love us — and so will you.

4.9/5

App Store

4.8/5

Google Play

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Basil

Android user

David K

iOS user

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

Rohan U

Android user

Xander S

iOS user

Elisha

iOS user

Paul T

iOS user

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Basil

Android user

David K

iOS user

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

Rohan U

Android user

Xander S

iOS user

Elisha

iOS user

Paul T

iOS user