Edexcel IGCSE Math A 4.8.C Two-Dimensional Trigonometry Problems

Practise selecting sine, cosine or tangent in multi-step triangles, bearings and composite-shape problems.

Exam points

identify a right triangle and label opposite, adjacent and hypotenuse for the target angle
use a bearing or parallel-line fact to derive the angle needed for trigonometry
carry an unrounded trigonometric result into a second perimeter or area calculation

[Maximum number: 5]

The diagram shows the positions of three villages, A, B and C

Figure for Question 4.8.C Two-dimensional trigonometry and bearings question 1 — Edexcel IGCSE Math A Higher

The bearing of B from A is $054^{\circ}$
The bearing of C from B is $132^{\circ}$
Melur walks from A to B
She then walks from B to C and from C to A
Melur walks at an average speed of $6 \mathrm{~km} / \mathrm{h}$
Work out the total time Melur takes.
Give your answer in hours and minutes.
hours
minutes

Angle:
$\angle ABC=54^\circ+(180^\circ-132^\circ)=102^\circ$

Cosine rule:
$AC=\sqrt{3.6^{2}+8.4^{2}-2(3.6)(8.4)\cos102^\circ} = 9.802\ldots$

Total time:
$\frac{9.802\ldots+8.4+3.6}{6}=3.633\ldots\text{ h}$

Final answer:
$3\text{ hours }38\text{ minutes}$

Accept 3 hours and 37 to 38 minutes.

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4.8.C Two-dimensional trigonometry and bearings question 1