ECZ 2025 · GCE Paper 2 · Question 8 — Trigonometry

A garden is in the form of a quadrilateral PQRS with PQ = 5m, QR = 8m, RS = 7m and PS = 6m; angle PQR = 140° and angle PRS = 18°.

(a(i)) Calculate PR.[5]

Verified working — step 1

In triangle PQR, use the Cosine Rule:

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

Verified working — step 1

Area of triangle PRS = 12× PR × RS × sin(PRS)

(a(iii)) Calculate the shortest distance from S to PR.[2]

Verified working — step 1

Let h = shortest distance from S to PR.

(b) Solve the equation 10 tan θ = 50 for 0° ≤ θ ≤ 90°.[1]

Verified working — step 1

10 tanθ = 50

(c) Simplify 9a - c81a^2 - c^2.[2]

Verified working — step 1

9a - c81a^2 - c^2

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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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