GCSE Maths Practice: bearings

Question 7 of 10

This question introduces resolving a distance into its eastward component using bearings and sine.

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\( \begin{array}{l}\text{A plane flies 200 km from A to B on a bearing of } 030^\circ.\\ \text{Find the Eastward distance travelled.}\end{array} \)

Choose one option:

Draw the triangle, identify the eastward side as opposite, and use sine.

When a plane flies on a bearing, it travels along a straight path at a certain angle from North. To find how far it travels East, we resolve the distance along the east-west axis. Using trigonometry, the eastward distance = total distance × sin(angle from North). Here, a plane flies 200 km at 030° bearing. The eastward distance is 200 × sin(30°) = 100 km. This approach applies to all bearings: use sine for perpendicular components and cosine for adjacent components. Students should visualise the triangle formed by the movement, label sides and angles, and apply sine or cosine accordingly. Practising multiple bearings improves understanding of navigation, coordinate geometry, and real-world applications. Accurate calculation ensures confidence in resolving distances in vector and bearings problems.