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WMA11/01 Jun 2019, Question 7: Triangles and Sectors in Radians

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 10 marks

The question, in short

Figure shows sector ABCOA of a circle radius 6 cm joined to triangle AOD, with D on OC, AD = 5 cm and angle AOD = 0.7 rad. Find sector area, angle ADO, then perimeter of ABCDA.

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

Part (a) · 3 marks

Calculate the area of sector ABCOA using radius 6 cm and angle 0.7 radians, giving the result to one decimal place.

  1. 1The sector angle is the reflex angle 2π − 0.7
  2. 2Area = ½ × 6² × (2π − 0.7)
  3. 3= 18 × 5.5832 = 100.5 cm²

Answer100.5 cm²

Part (b) · 3 marks

Using AD = 5 cm, OA = 6 cm and angle AOD = 0.7 rad, find the obtuse angle ADO to 3 decimal places.

  1. 1Sine rule in triangle AOD: sin ADO/6 = sin 0.7/5
  2. 2sin ADO = 6 sin 0.7/5 = 0.773…
  3. 3ADO is obtuse: ADO = π − 0.8837… = 2.258 rad

AnswerAngle ADO = 2.258 rad

Part (c) · 4 marks

Hence work out the perimeter of shape ABCDA, including arc ABC, CD, DA, to one decimal place.

  1. 1Arc ABC = 6(2π − 0.7) = 33.50 cm
  2. 2Angle OAD = π − 0.7 − 2.258 = 0.1837 rad
  3. 3OD = 5 sin 0.1837/sin 0.7 = 1.42 cm, so DC = 6 − 1.42 = 4.58 cm
  4. 4Perimeter = 33.50 + 4.58 + 5 = 43.1 cm

Answer43.1 cm

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Also searched as: WMA11 June 2019 · WMA11/01 · wma11 jun19 · IAS Maths Pure Mathematics 1 June 2019 · question 7.
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