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4024/21 May/Jun 2023, Question 7: The Sine Rule

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 13 marks

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The question, in short

Construct triangle ABC from given side and angle, measure to find its perimeter, then use a quadrilateral diagram with SQ = 15 cm to calculate lengths PS, SR and QR.

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

Part (ai) · 2 marks

Draw triangle ABC using the given line AB, with AC = 8.3 cm and angle BAC = 105°.

  1. 1At A, measure an angle of 105° from AB with a protractor and draw a line
  2. 2Mark C on this line with AC = 8.3 cm
  3. 3Join B to C

AnswerCorrect triangle

Part (aii) · 2 marks

Measure the unknown sides of your constructed triangle and work out its perimeter.

  1. 1Measure AB and BC on your triangle (AB + AC comes to 17.1 to 17.5 cm)
  2. 2Perimeter = AB + BC + 8.3
  3. 3Perimeter = 30.8 to 31.2 cm

Answer30.8 to 31.2

Part (bi) · 3 marks

Using SQ = 15 cm, angle SPQ = 67° and angle PQS = 74°, calculate the length PS.

  1. 1PS/sin 74° = 15/sin 67°
  2. 2PS = 15 × sin 74°/sin 67°
  3. 3PS = 15.66… ≈ 15.7 cm

Answer15.7 or 15.66…

Part (biia) · 3 marks

Given angle PSR = 96° and triangle QRS area 63 cm², show that SR rounds to 10.0 cm.

  1. 1Angle PSQ = 180 − 67 − 74 = 39°
  2. 2Angle QSR = 96 − 39 = 57°
  3. 31/2 × 15 × SR × sin 57° = 63
  4. 4SR = 126/(15 × sin 57°) = 10.01… = 10.0 cm (1 d.p.)

Answer10.01 to 10.02

Part (biib) · 3 marks

Using your value of SR and the given information, calculate the length QR.

  1. 1QR² = 15² + 10² − 2 × 15 × 10 × cos 57°
  2. 2QR² = 325 − 163.39… = 161.6…
  3. 3QR = √161.6… = 12.71… ≈ 12.7 cm

Answer12.7 or 12.71 to 12.72…

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Also searched as: 4024/21/M/J/23 · 4024_s23_qp_21 · 4024 s23 21 · question 7.
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