Video: GCSE Mathematics Foundation Tier Pack 2 • Paper 2 • Question 18

GCSE Mathematics Foundation Tier Pack 2 • Paper 2 • Question 18

02:12

Video Transcript

The diagram shows the position of town A and town B. Ezra thinks that the bearing of town B from town A is 115 degrees. Explain why Ezra is wrong.

To answer this question, we need to remember some key facts about bearings. Bearings are measured in degrees and they’re always measured in a clockwise direction from north. We also need to be clear what is meant by the bearing of one point or place from another point or place.

If we’re describing the bearing of town B from town A, this means that we’re starting at town A. We then face north and turn in a clockwise direction until we’re facing directly towards point B. The angle representing the bearing of town B from town A will, therefore, be the angle that I have marked in blue.

Now, Ezra says that this bearing is 115 degrees. But if we look at this angle, we can see that it is a reflex angle. It’s more than 180 degrees. This is because the bearing of a point directly south of A would be 180 degrees as there are 180 degrees on a straight line. However, this bearing is more than that. An answer of 115 degrees which is an obtuse angle will clearly then not be correct.

In fact, what Ezra has done is given the angle that has been marked on the diagram, which would be correct if bearings were measured in an anticlockwise direction rather than a clockwise direction. The true bearing can be found by subtracting 115 degrees from 360 degrees as there are 360 degrees around a point.

The correct bearing of town B from town A is 245 degrees. So we can answer that the reason Ezra is wrong is because bearing should always be measured clockwise from north, whereas Ezra has measured in an anticlockwise direction.

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