GCSE Maths Practice: bearings

Question 6 of 10

This question extends eastward distance calculation to a different bearing.

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\( \begin{array}{l}\text{A plane flies 300 km on a bearing of 045^\circ.\\ Find its Eastward distance travelled (to 1 decimal place).}\end{array} \)

Choose one option:

Use a triangle, identify opposite side, and apply sine. Round as instructed.

When a plane flies at a 45° bearing, we resolve its path into eastward and northward components. The eastward distance is the side opposite the angle in the right-angled triangle formed by the path. Using sine: eastward distance = total distance × sin(45°). For 300 km, eastward distance = 300 × sin(45°) ≈ 212.1 km. Understanding sine and cosine for bearings allows students to solve navigation problems, coordinate movements, and vector decomposition. Visual diagrams help internalise components. Practise with various bearings and distances to develop confidence. This method applies to aviation, sailing, and map-based exercises. Always round appropriately when required, and double-check calculations using a calculator for accuracy.