0580/12 May/Jun 2022, Question 24: Using Trigonometry and Pythagoras Together
Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Calculator · 4 marks
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The question, in short
Using the two right-angled triangles ABD and BCD, with AD = 5 m, DC = 14 m and angle BAD = 53°, work out the length BC.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1tan 53° = BD/5, so BD = 5 tan 53° = 6.635…
- 2BC² = 14² + 6.635…²
- 3BC = √(196 + 44.02…) = √240.02…
- 4= 15.49… ≈ 15.5 m
Answer15.5 or 15.49…
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