ECZ 2022 · GCE Paper 2 · Question 8 — Trigonometry

In the diagram, triangle XYZ has XY = 6cm, angle YXZ = 60° and angle XYZ = 80°.

(a(i)) Calculate the length of YZ.[4]

Verified working — step 1

In triangle XYZ, angle XZY = 180° - 60° - 80° = 40°.

(a(ii)) Calculate the area of triangle XYZ.[2]

Verified working — step 1

Use Area = 12× XY × YZ × sin(Y), since angle Y lies between sides XY and YZ.

(a(iii)) Calculate the shortest distance from X to YZ.[2]

Verified working — step 1

Let h be the shortest distance from X to YZ (the height onto base YZ).

(b) Solve the equation tan θ = 2.75 for 0° ≤ θ ≤ 360°.[2]

Verified working — step 1

tanθ = 2.75

(c) Simplify 1 - 4x^21 + 2x.[2]

Verified working — step 1

1 - 4x² is a difference of two squares:

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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