Bearing

This item is taken from IGCSE Mathematics (0580) Paper 32 of October/November 2012.

To deal with this item, let us summarize the details of the problem:
   (a) Syllabus area: Trigonometry
   (b) Specific topic: Bearing

Since the bearing is from B, let us draw/highlight the north line on B.

The north line is the initial (starting) side of the angle for the bearing. Now, let us also identify the terminal (end) side of the angle. Just simply connect points A and B.

With the north line on B as the initial side and the line connecting A and B as the terminal side, we can now determine the angle of the bearing.

To solve for this. Let us take note that the given angle is on point A. Let us also take note that the north lines drawn from each point are parallel.

With the north lines parallel, the line connecting the two points A and B will serve as a transversal.

On parallel lines cut by a transversal, the interior angles on the same side of the transversal are supplementary.

It means that the measure of the other interior angle is 180 - 72 = 108 degrees.

Take note that the angle measuring 108 degrees and the bearing of A from B forms one whole revolution, which means that their sum is 360 degrees.

We can now find the bearing of A from B by subtracting 108 degrees from 360 degrees. That is 360 - 108 = 252 degrees.

Therefore, the bearing of A from B is 252 degrees.

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