Bearings & Constructions (DP IB Applications & Interpretation (AI)): Revision Note

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Bearings

What are bearings?

  • Bearings are a way of describing directions using angles

  • Bearings follow three rules:

    • They are measured from the North direction

      • An arrow showing the North line should be included on the diagram

    • They are measured clockwise

    • The angle is always written in 3 figures

      • If the angle is less than 100° the first digit will be a zero

How can I use bearings with trigonometry?

  • A question might give you:

    • at least three locations

    • bearings between some of the locations

    • distances between some of the locations

  • You might have to find a missing distance or bearing

  • Draw a triangle between the three relevant locations

  • Label any known distances and angles

    • You might have to subtract a bearing from 360° or another angle to find the angle in the triangle

  • Use the sine and/or cosine rule to find the required answer

Examiner Tips and Tricks

Always draw a big, clear diagram and annotate it, be especially careful to label the angles in the correct places!

Worked Example

The point B is 7 km from A on a bearing of 105°. The distance from B to C is 5 km and the bearing from B to C is 230°.  Find the distance from A to C.

3-3-3-ai-sl-bearings-we-solution-i

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Constructing Diagrams

What diagrams do I need to construct?

  • You are expected to construct diagrams based on information given

  • The information might include compass directions, bearings, angles

  • Look out for the plane the diagram should be drawn in

    • It will either be horizontal (something occurring at sea or on the ground)

    • Or it will be vertical (Including height)

  • Work through the statements given in the instructions systematically

What do I need to know?

  • You are just required to draw sketches

    • However, the more accurate your diagram is the easier it is to work with

  • Make sure you know your compass directions

    • Due east means on a bearing of 090°

      • Draw the line directly to the right

    • Due south means on a bearing of 180°

      • Draw the line vertically downwards

    • Due west means on a bearing of 270°

      • Draw the line directly to the left

    • Due north means on a bearing of 360° (or 000°)

      • Draw the line vertically upwards

  • Using the above bearings for compass directions will help you to estimate angles for other bearings on your diagram

Examiner Tips and Tricks

Draw your diagrams in pencil so that you can easily erase any errors.

Worked Example

A city at B is due east of a city at A and A is due north of a city at E. A city at C is due south of B.

The bearing from A to D is 155° and the bearing from D to C is 30°.

The distance AB = 50 km, the distances BC = CD = 30 km and the distances DE = AE = 40 km.

Draw and label a diagram to show the cities A, B, C, D and E and clearly mark the bearings and distances given.

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Amber

Author: Amber

Expertise: Maths Content Creator

Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.

Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Subject Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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