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4024/22 May/Jun 2021, Question 7: Choosing the Right Trigonometric Ratio

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 13 marks

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The question, in short

Three-part geometry question: rectangle perimeter and diagonal, a triangle with sides a, a+4, 11 and a 60° angle, and a quadrilateral with given sides and area.

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

Part (ai) · 1 mark

Find the perimeter of a 30 m by 45 m rectangle.

  1. 1Perimeter = 2 × (30 + 45)
  2. 2= 150 m

Answer150

Part (aii) · 2 marks

Find the diagonal length of the 30 m by 45 m rectangle.

  1. 1d² = 30² + 45² = 2925
  2. 2d = √2925 = 54.08… ≈ 54.1 m

Answer54.1 or 54.08…

Part (b) · 4 marks

In triangle PQR, PR = a, PQ = a + 4, RQ = 11 and angle PRQ = 60°. Find a.

  1. 1(a + 4)² = a² + 11² − 2 × a × 11 × cos 60°
  2. 2a² + 8a + 16 = a² + 121 − 11a
  3. 319a = 105
  4. 4a = 105/19 = 5 10/19

Answer5 10/19 or 5.53 or 5.526…

Part (c) · 6 marks

Quadrilateral ABCD has AC = 8, DC = 10, AB = 9, a right angle at C, and area 70 cm². Find angle DAB.

  1. 1Angle DAC = tan⁻¹(10/8) = 51.34…°
  2. 2Area ACD = 1/2 × 10 × 8 = 40 cm², so area ABC = 70 − 40 = 30 cm²
  3. 31/2 × 8 × 9 × sin CAB = 30 → sin CAB = 30/36 → angle CAB = 56.44…°
  4. 4Angle DAB = 51.34 + 56.44 = 107.78…° ≈ 107.8°

Answer107.8 or 107.78 to 107.79…

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