Trigonometry: sine rule — KCSE Mathematics

KCSE Mathematics · 100 practice questions · 3 syllabus objectives

34 easy33 medium33 hard

What You'll Learn

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

State the sine rule: a/sin A = b/sin B = c/sin C, and identify when to apply it (given AAS, ASA or SSA)

Apply the sine rule to find unknown sides and angles in non-right-angled triangles; handle the ambiguous case

Trigonometry: sine rule

Sample Questions

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1
easySHORT ANSWER4 marks

State the steps to find the length of side c in triangle XYZ, where angle X = 45°, angle Y = 60°, and side y = 9 cm. Justify whether the sine rule can be applied in this scenario. (4 marks)

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Part (a) — 3 marks
Calculate angle Z using the fact that the angles in a triangle sum to 180° (1 mk)
Use the sine rule: y/sin(Y) = c/sin(C) (1 mk)
Substitute the known values and solve for c (1 mk)
Part (b) — 1 mark
Yes, the sine rule can be applied as two angles and a side are known (1 mk)
2
easySHORT ANSWER3 marks

Explain how to determine the angle opposite side a in triangle ABC, where side a = 8 cm, side b = 10 cm, and angle B = 30°. Discuss if there is a possibility of more than one solution for angle A. (3 marks)

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Part (a) — 2 marks
Use the sine rule: a/sin(A) = b/sin(B) (1 mk)
Substitute values and solve for sin(A) (1 mk)
Part (b) — 1 mark
Yes, there could be two possible angles for A due to the sine function (1 mk)
3
easySHORT ANSWER4 marks

State the sine rule and identify two specific cases where it can be applied in triangle XYZ. (4 marks)

View Marking Scheme
Part (a) — 1 mark
a/sin A = b/sin B = c/sin C (or equivalent reciprocal form) (1 mk)
Part (b) — 3 marks
AAS (Angle-Angle-Side) (1 mk)
ASA (Angle-Side-Angle) (1 mk)
SSA (Side-Side-Angle) (1 mk)
4

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

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