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WMA11/01 Jan 2021, Question 5: Radians, Arcs and Sectors

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 9 marks

The question, in short

Solve triangle and sector problems for a viewing platform: find an obtuse angle, an arc length and a total area using 6 m radii, 14 m side and 0.43 radians.

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

Part (a) · 3 marks

Use the triangle with sides 6 m and 14 m and angle 0.43 radians to calculate the obtuse angle at O in radians.

  1. 1Sine rule in triangle AOD: sin(AOD)/14 = sin 0.43/6
  2. 2sin(AOD) = 14 sin 0.43 / 6 = 0.9726
  3. 3arcsin gives 1.337 (acute)
  4. 4AOD is obtuse, so AOD = π − 1.337 = 1.805

Answer1.805 radians

Part (b) · 2 marks

Calculate the length of the major arc from A through B to C using the radius 6 m.

  1. 1Arc ABC subtends the reflex angle AOC = 2π − 1.805 = 4.478
  2. 2Arc = 6 × 4.478
  3. 3= 26.9 m

Answer26.9 m

Part (c) · 4 marks

Calculate the combined area of the major sector and the triangle, giving the total in m².

  1. 1Sector area = ½ × 6² × 4.478 = 80.6
  2. 2Angle OAD = π − 1.805 − 0.43 = 0.907
  3. 3Triangle AOD = ½ × 6 × 14 × sin 0.907 = 33.1
  4. 4Total = 80.6 + 33.1 = 113.7 m²

Answer113.7 m²

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Also searched as: WMA11 January 2021 · WMA11/01 · wma11 jan21 · IAS Maths Pure Mathematics 1 January 2021 · question 5.
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