4024/22 May/Jun 2024, Question 10: The Cosine Rule
Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 7 marks
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The question, in short
A pentagon has four given interior angles; find the fifth, then use two side lengths from a vertex to work out a third side to 1 decimal place.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 2 marks
Work out the size of the interior angle at vertex B.
- 1Pentagon angle sum = (5 − 2) × 180 = 540°
- 2B = 540 − 106 − 148 − 79 − 120 = 87°
Answer87
Part (b) · 5 marks
Given AE = 8 cm and AD = 15 cm, find ED, showing working, rounded to 1 decimal place.
- 1Angle AED = 120°; let ED = x
- 215² = 8² + x² − 2 × 8 × x × cos 120°
- 3225 = 64 + x² + 8x, so x² + 8x − 161 = 0
- 4x = (−8 + √(64 + 644))/2 = (−8 + √708)/2 = 9.304…
- 5ED ≈ 9.3 cm
Answer9.3
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Also searched as: 4024/22/M/J/24 · 4024_s24_qp_22 · 4024 s24 22 · question 10.
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