Determining Final Position Using Bearings

00:00 4 marks

A ship departs from port A and sails 5 km on a bearing of 045°. It then changes course and sails 8 km on a bearing of 120°. Assuming port A is at the origin with east as the positive x-direction and north as the positive y-direction, determine the final coordinates of the ship.

Hint Hint

Hint

Consider resolving each leg of the journey into eastward (x) and northward (y) components using trigonometry and bearing angles. Recall the trigonometric relationships in a right-angled triangle to resolve each leg of the journey into its x and y components.

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Answer Answer

Complete Answer

The final coordinates are approximately \((10.46, -0.46)\) km.

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