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4MA1/1H Nov 2021, Question 12: Angles of Elevation and Depression

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 6 marks

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The question, in short

Using a 100 m cliff, buoy distance d, and elevation angles of 20° to the cliff top and 25° to mast top A, find d and the mast height, each to 3 significant figures.

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

Part (a) · 3 marks

Calculate the horizontal distance d from the buoy to the cliff base using the 100 m cliff height and 20° elevation angle; give to 3 significant figures.

  1. 1100 m is opposite the 20° angle and d is adjacent
  2. 2tan 20° = 100/d, so d = 100 ÷ tan 20°
  3. 3d = 274.7… = 275 (3 s.f.)

Answer275

Part (b) · 3 marks

Calculate the height of the radio mast above the cliff using the 25° elevation angle and the distance d; give to 3 significant figures.

  1. 1Height of A above sea: tan 25° = (100 + h)/274.7…
  2. 2100 + h = 274.7… × tan 25° = 128.1…
  3. 3h = 128.1… − 100 = 28.1 m

Answer28.1

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