0580/42 Oct/Nov 2023, Question 6: Using Trigonometry and Pythagoras Together
Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 7 marks
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The question, in short
Right-angled triangle with sides t cm, 5 cm and hypotenuse (2t + 3) cm; angle w° between hypotenuse and the 5 cm side. Find w.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 7 marks
- 1(2t + 3)² = t² + 5²
- 24t² + 12t + 9 = t² + 25, so 3t² + 12t − 16 = 0
- 3t = (−12 + √(12² − 4(3)(−16)))/(2 × 3) = (−12 + √336)/6 = 1.0550…
- 4tan w = t/5 = 1.0550…/5
- 5w = 11.91… ≈ 11.9
Answer11.9 or 11.91 to 11.92
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Also searched as: 0580/42/O/N/23 · 0580_w23_qp_42 · 0580 w23 42 · question 6.
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