ECZ 2023 · GCE Paper 2 · Question 7 — Trigonometry

Positions of three towns P, Q and R: PQ = 7.1km, PR = 23.8km and angle RPQ = 92.7°.

(a(i)) Calculate the distance RQ to 2 decimal places.[5]

Verified working — step 1

Use the Cosine Rule:

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

Verified working — step 1

Area = 12(PQ)(PR) sin(RPQ)

(a(iii)) Calculate the shortest distance of P from RQ giving your answer to 2 decimal places.[2]

Verified working — step 1

Let h = shortest distance from P to RQ.

(b) Solve the equation 3 tan θ = 89 for 0° ≤ θ ≤ 180°.[1]

Verified working — step 1

3 tanθ = 89

(c) Simplify 9x^2 - 19x + 3.[2]

Verified working — step 1

Numerator: 9x² - 1 = (3x - 1)(3x + 1) [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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