# Bearings

## Practise your ability to interpret and use three-figure bearings with this self-marking exercise.

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This is level 5: using angle theorems and trigonometry to solve bearing problems. You can earn a trophy if you get at least 7 correct and you do this activity online.

Give answers correct to the nearest degree.

 A small passenger plane flies 6km due north then 10km due east. What is the three figure bearing of its current position from its starting position? ° Oblong lake is in the shape of a rectangle 3km by 2km. The longest sides run east-west. What is the three figure bearing of the south-east corner from the north-west corner? ° A speedboat travels 6km due east then 5km due north. What bearing would it travel on to get back to its starting point? ° In the remote desert strange scorch marks have been found. They are very regularly positioned as a square grid with each mark 1km from the next in a north-south and east-west direction. The marks have each been numbered by investigators and a part of their map is shown above. The following questions refer to this map. What is the bearing of mark 53 from mark 72? ° What is the bearing of mark 77 from mark 64? ° What is the bearing of mark 52 from mark 75? ° A straight road runs from A to B on a bearing of 044°. Another straight road runs from B to C on a bearing of 134°. Calculate angle BCA if AB = 7kmand BC = 8km. ° A ship turns left through a right angle after having been sailing on a bearing of 350° for 10km. It sails for 8km in this new direction. On what bearing must it sail to get back to its starting point? ° A helicopter flies 50km on a bearing of 048° and then 120km on a bearing of 138° How far is it from its starting position? km
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This is Bearings level 5. You can also try:
Level 1 Level 2 Level 3 Level 4

## Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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#### Where's Wallaby?

Find the hidden wallaby using the clues revealed at the chosen coordinates. Not only is this a fun way to practise using coordinates it is also a great introduction to Pythagoras' theorem and loci.

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## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

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Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

## Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

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Transum,

Monday, July 24, 2017

"This is a page from a Scout's notebook written around 1966.

"

Colin, Home

Thursday, November 23, 2017

"On bearings level 3 question 6. the opposite bearing of 208 degrees is 028 degrees. your answer is 28 degrees. you only have 2 digits.

[Transum: Thanks so much Colin, for highlighting this error. The questions are generated from random numbers and the algorithm used in question 6 missed the three digit rule. The bug has now been eliminated. I hope your students enjoy this exercise.]"

Lahi, New Zealand

Wednesday, October 20, 2021

"There seems to be a problem with the question: "What is the three figure bearing of east?" and "What is the three figure bearing of north-east?". If I am correct the answer to the first one is 90 degrees and the other one is 45 degrees. But when I answer it the system says it's wrong. If this is because I got the answer wrong my apologies. Thanks in advance!

[Transum: You are almost correct Lahi but you need to think about the words “three figure” in the question]"

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

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Scan the QR code below to visit the online version of this activity.

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Before beginning these exercises it would be helpful to develop bearing estimation skills with the Plane Bearings activity.

Level 1 - Converting between compass directions and three figure bearings

Level 2 - Measuring simple bearings on screen using a draggable protractor

Level 3 - Back bearings and turning problems

Level 4 - Creating scale diagrams and making accurate measurements of given situations

Level 5 - Using angle theorems and trigonometry to solve bearing problems

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

After working hard on these exercises treat yourself to some relaxation playing Snooker Angles.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

## Compass Points

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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