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Maths
14 Dec 2025
2,038
4 pages
Shaz @shaz2007
This comprehensive guide covers bearings calculations and scale drawings for navigation. It provides step-by-step instructions, examples, and key... Show more
This page delves into more complex bearing calculations, including return bearings and multi-step problems.
Example A walker travels 1200 m on a bearing of 165° and then another 1500 m on a bearing of 210°. The problem asks to find the distance from the starting point and the bearing to return to base.
The page demonstrates how to use scale drawings and trigonometric calculations to solve such problems. It introduces the concept of supplementary angles and the use of the cosine rule for non-right-angled triangles.
Highlight When solving complex bearing problems, you may need to use Pythagoras theorem for right-angled triangles or the cosine rule for non-right-angled triangles.
This section is particularly useful for students preparing for trigonometry bearings questions and answers pdf and GCSE maths bearings and distance problems with solutions.
This page focuses on using the cosine rule to solve a complex bearing problem.
Definition Cosine Rule a² = b² + c² - 2bc cos A, where A is the angle opposite side a in a triangle.
The page provides a step-by-step solution to find the return bearing in the walker problem introduced on the previous page. It demonstrates how to set up the cosine rule equation, solve for the angle, and then use this information to calculate the final bearing.
Highlight To find a return bearing, subtract the calculated angle from 360°.
This detailed explanation is invaluable for students working on bearings Maths GCSE questions and answers and IGCSE bearing questions and answers PDF.
The final page presents two complex bearing problems that integrate various concepts covered in the previous pages.
Problem 1 involves a coastguard spotting a boat and a tree, requiring students to draw a scale diagram and use Pythagoras theorem to verify their measurements.
Example A coastguard spots a boat on a bearing of 040° and at a distance of 350 m. He can also see a tree due east of him. The tree is due south of the boat.
Problem 2 is a more complex scenario involving four towns and their relative positions using bearings and distances.
Highlight When solving multi-step bearing problems, choose an appropriate scale for your diagram to ensure accuracy in measurements.
These problems provide excellent practice for students preparing for GCSE maths bearings and distance problems worksheets and measuring bearings using angles GCSE questions and answers.
This page introduces the fundamental concepts of bearings in mathematics.
Definition Bearings are always measured from a North line clockwise and are given as 3-digit numbers.
Example 18° is written as 018° in bearing notation.
The page explains how to calculate bearings in various diagrams, emphasizing the importance of drawing a North line when it's not provided. It also covers the concept of allied angles and angles around a point.
Highlight To find a bearing, remember that angles around a point add up to 360°, and allied angles add up to 180°.
Vocabulary Allied angles - Two angles that add up to 180°.
This information is crucial for students tackling bearings GCSE maths grade 8 questions and answers.
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.
59
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore essential GCSE exam questions on bearings and trigonometry. This resource covers angle measurement, distance calculations, and trigonometric formulas, providing clear examples and solutions to enhance your understanding. Ideal for students preparing for their exams.
MathsExplore essential techniques for constructing geometric loci and bisectors using a ruler and compass. This summary covers key concepts such as perpendicular bisectors, angle bisectors, and the properties of loci, complete with step-by-step examples tailored for GCSE students.
MathsMaster the technique of constructing perpendicular bisectors with this detailed guide. This resource covers step-by-step instructions for drawing perpendicular bisectors from points and lines, essential for GCSE Maths constructions. Ideal for students preparing for exams, this summary emphasizes key concepts and practical applications.
MathsGCSE maths foundation/higher averages:mean, median, model, range, sequences, and area equations
MathsExplore the Pythagorean Theorem with detailed examples and exercises. This resource covers calculating hypotenuse lengths, understanding right triangles, and applying the theorem in real-world contexts. Ideal for higher maths students seeking clarity on key concepts like special right triangles, distance formulas, and triangle construction.
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
Shaz
@shaz2007
This comprehensive guide covers bearings calculations and scale drawings for navigation. It provides step-by-step instructions, examples, and key concepts for accurately measuring and calculating bearings.
• Explains how bearings are measured clockwise from North using 3-digit numbers
• Demonstrates techniques... Show more
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page delves into more complex bearing calculations, including return bearings and multi-step problems.
Example: A walker travels 1200 m on a bearing of 165° and then another 1500 m on a bearing of 210°. The problem asks to find the distance from the starting point and the bearing to return to base.
The page demonstrates how to use scale drawings and trigonometric calculations to solve such problems. It introduces the concept of supplementary angles and the use of the cosine rule for non-right-angled triangles.
Highlight: When solving complex bearing problems, you may need to use Pythagoras theorem for right-angled triangles or the cosine rule for non-right-angled triangles.
This section is particularly useful for students preparing for trigonometry bearings questions and answers pdf and GCSE maths bearings and distance problems with solutions.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page focuses on using the cosine rule to solve a complex bearing problem.
Definition: Cosine Rule: a² = b² + c² - 2bc cos A, where A is the angle opposite side a in a triangle.
The page provides a step-by-step solution to find the return bearing in the walker problem introduced on the previous page. It demonstrates how to set up the cosine rule equation, solve for the angle, and then use this information to calculate the final bearing.
Highlight: To find a return bearing, subtract the calculated angle from 360°.
This detailed explanation is invaluable for students working on bearings Maths GCSE questions and answers and IGCSE bearing questions and answers PDF.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The final page presents two complex bearing problems that integrate various concepts covered in the previous pages.
Problem 1 involves a coastguard spotting a boat and a tree, requiring students to draw a scale diagram and use Pythagoras theorem to verify their measurements.
Example: A coastguard spots a boat on a bearing of 040° and at a distance of 350 m. He can also see a tree due east of him. The tree is due south of the boat.
Problem 2 is a more complex scenario involving four towns and their relative positions using bearings and distances.
Highlight: When solving multi-step bearing problems, choose an appropriate scale for your diagram to ensure accuracy in measurements.
These problems provide excellent practice for students preparing for GCSE maths bearings and distance problems worksheets and measuring bearings using angles GCSE questions and answers.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page introduces the fundamental concepts of bearings in mathematics.
Definition: Bearings are always measured from a North line clockwise and are given as 3-digit numbers.
Example: 18° is written as 018° in bearing notation.
The page explains how to calculate bearings in various diagrams, emphasizing the importance of drawing a North line when it's not provided. It also covers the concept of allied angles and angles around a point.
Highlight: To find a bearing, remember that angles around a point add up to 360°, and allied angles add up to 180°.
Vocabulary: Allied angles - Two angles that add up to 180°.
This information is crucial for students tackling bearings GCSE maths grade 8 questions and answers.
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.
59
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore essential GCSE exam questions on bearings and trigonometry. This resource covers angle measurement, distance calculations, and trigonometric formulas, providing clear examples and solutions to enhance your understanding. Ideal for students preparing for their exams.
MathsExplore essential techniques for constructing geometric loci and bisectors using a ruler and compass. This summary covers key concepts such as perpendicular bisectors, angle bisectors, and the properties of loci, complete with step-by-step examples tailored for GCSE students.
MathsMaster the technique of constructing perpendicular bisectors with this detailed guide. This resource covers step-by-step instructions for drawing perpendicular bisectors from points and lines, essential for GCSE Maths constructions. Ideal for students preparing for exams, this summary emphasizes key concepts and practical applications.
MathsGCSE maths foundation/higher averages:mean, median, model, range, sequences, and area equations
MathsExplore the Pythagorean Theorem with detailed examples and exercises. This resource covers calculating hypotenuse lengths, understanding right triangles, and applying the theorem in real-world contexts. Ideal for higher maths students seeking clarity on key concepts like special right triangles, distance formulas, and triangle construction.
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