4024/22 Oct/Nov 2022, Question 7: The Cosine Rule
Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 8 marks
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The question, in short
For a quadrilateral floor plan with sides AB = 95, BC = 107, CD = 165, AD = 160 and a right angle at A, find an angle and a related elevation angle.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 4 marks
Find the size of angle BCD in the quadrilateral, using the given side lengths in metres.
- 1BD² = 160² + 95² = 34 625
- 2cos BCD = (107² + 165² − 34 625)/(2 × 107 × 165)
- 3= 4049/35 310 = 0.1146…
- 4Angle BCD = 83.41… ≈ 83.4°
Answer83.4 or 83.36 to 83.43
Part (b) · 4 marks
A light hangs vertically above B; from C its elevation is 8.2°. Find the elevation angle of the same light measured from A.
- 1Height of light = 107 × tan 8.2° = 15.41… m
- 2tan θ = 15.41…/95
- 3θ = 9.218… ≈ 9.22°
Answer9.22 or 9.218 to 9.219…
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