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Trigonometry: cosine rule — KCSE Mathematics

KCSE Mathematics · 117 practice questions · 3 syllabus objectives

36 easy39 medium42 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

State the cosine rule: c² = a² + b² – 2ab cos C (and its rearrangement) and identify when to apply it (given SAS or SSS)

Apply the cosine rule to calculate unknown sides and angles in triangles; use the formula A = ½ab sin C for area

Trigonometry: cosine rule

Sample Questions

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1
easySHORT ANSWER3 marks

State the cosine rule and explain when it is applicable in triangle measurements. (3 marks)

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Part (a) — 1 mark
c² = a² + b² − 2ab cos C (1 mk)
Part (b) — 2 marks
Applicable when two sides and the included angle (SAS) are known (1 mk)
Also applicable when all three sides (SSS) are known (1 mk)
2
easySHORT ANSWER4 marks

In triangle XYZ, the lengths of sides XY and XZ are 8 cm and 6 cm respectively, with an included angle ∠Y measuring 45°. Determine the area of triangle XYZ using the formula A = ½ab sin C. (4 marks)

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Part (a) — 4 marks
Identify a = 8 cm, b = 6 cm, and C = 45° (1 mk)
Use the area formula: A = ½(8)(6)sin(45°) (1 mk)
Calculate the sine of 45°, which is √2/2 (1 mk)
Final area calculation: A = 24√2/2 = 12√2 cm² (approximately 16.97 cm²) (1 mk)
3
easySHORT ANSWER3 marks

In triangle PQR, side PQ measures 7 cm, side PR measures 5 cm, and the included angle ∠Q is 60°. Calculate the length of side QR using the cosine rule. (3 marks)

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Part (a) — 3 marks
Apply the cosine rule: QR² = PQ² + PR² - 2(PQ)(PR)cos(Q) (1 mk)
Substitute values: QR² = 7² + 5² - 2(7)(5)cos(60°) (1 mk)
Calculate QR and provide the final answer: QR = 6.32 cm (approximately) (1 mk)
4

State the rearranged form of the cosine rule and describe its use in calculating an angle in triangle XYZ. (4 marks)

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Why Practise Trigonometry: cosine rule?

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