GCSE Maths Practice: bearings

Question 5 of 10

This question requires combining multiple bearings to find a resultant direction.

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\( \begin{array}{l}\text{A ship sails 100 km NE, then 100 km SE.\\ Find the bearing of C from A.}\end{array} \)

Choose one option:

Resolve each leg into components, add east-west and north-south separately, then calculate resultant bearing.

When a ship sails on multiple legs with different bearings, the overall bearing from start to finish can be calculated using vector addition. Here, the ship goes 100 km NE, then 100 km SE. Eastward distances add, northward distances cancel. Resulting bearing from A to C is due East = 090°. Understanding this requires breaking each leg into north-south and east-west components using sine and cosine. Drawing a diagram of the movement helps visualise components and net direction. Mastery of resolving legs into components and combining them strengthens skills in bearings, navigation, and trigonometry. Practice with various bearings, distances, and angles improves accuracy in calculating resultant bearings and distances. This method is applicable in navigation, physics, and geometry.