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 question Non-right-angled triangles revision Revise the key idea

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Paper

Marks

Topic

Non-right-angled triangles

Exam-style question

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Paper 2Core or Extended Mathematics6 marks

Ambiguous case in triangle solving

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.

a
Calculate the possible lengths of side XZ.
Your answer
Aim for approximately 3 distinct marking points.
[3]
b
Explain why there is only one possible triangle in this case.
Your answer
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.
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Paper 2 structured question: Non-right-angled triangles

Paper 2Core or Extended Mathematics6 marks

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/Angle	Value
AB	7 cm
AC	10 cm
Angle BAC	120°

a
Calculate the length of side BC.
Your answer
Aim for approximately 3 distinct marking points.
[3]
b
Calculate the area of triangle ABC.
Your answer
Aim for approximately 3 distinct marking points.
[3]