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Fun with Bearings: Easy Scale Drawing, Maths Questions, and Measurement Tips

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Shaz

03/03/2023

Maths

Bearings Maths GCSE year 11

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Maths

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Geometry and measure

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Loci and constructions

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Bearings

Fun with Bearings: Easy Scale Drawing, Maths Questions, and Measurement Tips

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 for finding return bearings and allied angles
• Covers scale drawing methods for solving complex bearings problems
• Includes practice questions with detailed solutions using trigonometry and the cosine rule
• Provides tips on using Pythagoras' theorem to check scale drawing measurements

...

03/03/2023

1984

Bearings 10 Bearings are always measured from a Northline clockwise. N 3 (4) You need to draw. your north line in. before measuring a bearin

View

Page 2: Advanced Bearing Calculations

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.

Bearings 10 Bearings are always measured from a Northline clockwise. N 3 (4) You need to draw. your north line in. before measuring a bearin

View

Page 3: Applying the Cosine Rule in Bearing Problems

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.

Bearings 10 Bearings are always measured from a Northline clockwise. N 3 (4) You need to draw. your north line in. before measuring a bearin

View

Page 4: Practical Applications and Complex Problems

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.

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4 pages

Fun with Bearings: Easy Scale Drawing, Maths Questions, and Measurement Tips

user profile picture

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

Bearings 10 Bearings are always measured from a Northline clockwise. N 3 (4) You need to draw. your north line in. before measuring a bearin

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Page 2: Advanced Bearing Calculations

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.

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

Page 3: Applying the Cosine Rule in Bearing Problems

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.

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

Page 4: Practical Applications and Complex Problems

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.

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

Page 1: Introduction to Bearings

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.

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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

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

Thomas R

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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.

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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.

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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

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Xander S

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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

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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

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