Lemmara logoLemmaraWorked solution

WMA11/01 Oct 2021, Question 7: Triangles and Sectors in Radians

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

The question, in short

For a bird sanctuary sign made from kite OABC joined to major sector OCXA with OA = OC = 0.6 m, AB = CB = 1.4 m and angles OAB = OCB = 2 radians, work out θ, the perimeter and the area.

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

Part (a) · 4 marks

Show, with clear working, that the angle AOC = θ equals 1.64 radians to 3 significant figures.

  1. 1OB² = 0.6² + 1.4² − 2(0.6)(1.4)cos 2
  2. 2OB² = 3.019…, so OB = 1.738 m
  3. 3sin AOB / 1.4 = sin 2 / 1.738, so angle AOB = 0.822 rad
  4. 4θ = 2 × 0.822 = 1.64 rad (3 s.f.)

AnswerShown: OB = 1.738 m, angle AOB = 0.822 rad, so θ = 2 × 0.822 = 1.64 rad

Part (b) · 2 marks

Calculate the total perimeter of the sign in metres, giving the answer to 2 significant figures.

  1. 1Major arc angle = 2π − 1.64 = 4.643 rad
  2. 2Arc length = 0.6 × 4.643 = 2.786 m
  3. 3Perimeter = 2.786 + 1.4 + 1.4 = 5.6 m (2 s.f.)

Answer5.6 m

Part (c) · 4 marks

Calculate the total area of the sign in m², giving the answer to 2 significant figures.

  1. 1Sector area = ½ × 0.6² × (2π − 1.64) = 0.836 m²
  2. 2Kite area = 2 × ½ × 0.6 × 1.4 × sin 2 = 0.764 m²
  3. 3Total = 0.836 + 0.764 = 1.60
  4. 4Area = 1.6 m² (2 s.f.)

Answer1.6 m²

Stuck on a step? Read the free lesson: Triangles and Sectors in Radians

Practise more triangles and sectors in radians questions

Real XMA01 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on triangles and sectors in radians

Also searched as: WMA11 October 2021 · WMA11/01 · wma11 oct21 · IAS Maths Pure Mathematics 1 October 2021 · question 7.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.