4MA1/2HR Jun 2022, Question 10: Using Trigonometry and Pythagoras Together
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 5 marks
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The question, in short
In regular hexagon ABCDEF with triangle ABP inside, AB = 5 cm, BP = 2 cm and angle ABP = 90°, work out angle PAF to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1tan(BAP) = 2 / 5
- 2BAP = tan⁻¹(2 / 5)
- 3BAP = 21.801...
- 4Interior angle of regular hexagon = (6 − 2) × 180 / 6
- 5Interior angle = 720 / 6 = 120°
- 6Angle PAF = 120° − 21.801...
- 7Angle PAF = 98.198...
- 8Angle PAF = 98.2° (to 3 significant figures)
Answer98.2
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