A cyclist start from a point x and rides 3km due east to a point y. At y,he changes direction and rides 5km north west to a point z. Find the bearing of z from x to the nearest degree

Answer 1

To find the bearing of point z from point x, we need to determine the angle of the line connecting these two points with respect to the north direction.

First, we draw a diagram of the situation described:

N
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|
|
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Z ----X---- Y
E

We know that the cyclist rides 3km due east from point x to point y. This creates a right-angled triangle with its hypotenuse being the line XY. The angle between the line XY and the due east direction is 90°.

Next, the cyclist changes direction and rides 5km northwest from point y to point z. This creates a right-angled triangle with its hypotenuse being the line YZ. The northwest direction corresponds to the bearing of 315°.

Now, we can find the bearing of point z from point x by adding the two angles: 90° + 315° = 405°.

However, a bearing must be expressed within the range of 0° to 360°, so to find the bearing to the nearest degree, we need to subtract 360° from the calculated bearing: 405° - 360° = 45°.

Therefore, the bearing of point z from point x is 45° to the nearest degree.