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Cambridge IGCSE Mathematics practice

exam practice - Apply the sine and cosine rules to solve problems related to non-right-angled triangles, including those with obtuse angles and ambiguous cases. Use the formula for the area of a triangle, which is given as area = ab sin C. - Non-right-angled triangles

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Attempt questionNon-right-angled triangles revisionRevise the key idea

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2

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6

Marks

Topic

Non-right-angled triangles

Exam-style question

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Paper 2Core or Extended Mathematics6 marks

Solving a triangle with an obtuse angle

Diagram Description

Triangle ABC

Triangle ABC has sides AB = 7 cm, AC = 10 cm, and angle BAC = 120°. Find the length of side BC and the area of the triangle.

Side/AngleValue
AB7 cm
AC10 cm
Angle BAC120°
  1. a

    Calculate the length of side BC.

    Aim for approximately 3 distinct marking points.

    [3]
  2. b

    Calculate the area of triangle ABC.

    Aim for approximately 3 distinct marking points.

    [3]

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Maths method check

  • Topic focus: Non-right-angled triangles.
  • Question style: structured_mathematics.
  • Reasoning demand: reasoning.
  • Check the operation, notation, units, and final answer form against the question before moving on.

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Paper 2 structured question: Non-right-angled triangles

Paper 2Core or Extended Mathematics6 marks

Description

Triangle XYZ

In triangle XYZ, side XY = 8 cm, side YZ = 6 cm, and angle XYZ = 40°. Determine the possible lengths of side XZ and explain if there is more than one possible triangle.

  1. a

    Calculate the possible lengths of side XZ.

    Aim for approximately 3 distinct marking points.

    [3]
  2. b

    Explain why there is only one possible triangle in this case.

    Aim for approximately 3 distinct marking points.

    [3]