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4024/21 May/Jun 2024, Question 7: Choosing the Right Trigonometric Ratio

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 10 marks

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The question, in short

Cuboid volume gives h; pentagon with AE parallel BD, AE=21, BD=16, DE=8, right angle at E, angle CBD=65°: find angle BAE and BC given area 200 cm².

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

Cuboid measures 5 cm by 12 cm by h cm with volume 480 cm³; calculate h.

  1. 15 × 12 × h = 480
  2. 260h = 480, so h = 8

Answer8

Part (bi) · 3 marks

Pentagon ABCDE with AE parallel BD, AE=21, BD=16, DE=8, angle DEA=90°; calculate angle BAE.

  1. 1Horizontal distance = 21 − 16 = 5 cm, height = DE = 8 cm
  2. 2tan(BAE) = 8/5
  3. 3Angle BAE = 57.99… ≈ 58.0°

Answer58.0 or 57.99…

Part (bii) · 5 marks

Pentagon area is 200 cm²; using the given lengths and angle CBD=65°, calculate length BC.

  1. 1Area ABDE = 1/2 × (16 + 21) × 8 = 148 cm²
  2. 2Area BCD = 200 − 148 = 52 cm²
  3. 31/2 × 16 × BC × sin 65° = 52
  4. 4BC = 52/(8 sin 65°) = 7.171…
  5. 5BC ≈ 7.17 cm

Answer7.17 or 7.171 to 7.172

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