ECZ 2023 · GCE Paper 2 · Question 7 — Trigonometry
Question from ECZ 2023 · GCE Paper 2 · Question 7
(a) The diagram shows the positions of three towns P, Q and R. PQ = 7.1 km, PR = 23.8 km and angle RPQ = 92.7°. Calculate the
(a(i)) distance RQ to 2 decimal places,[5]
Verified working — step 1
Two sides and the included angle: cosine rule.(a(ii)) area of the triangle PQR,[2]
Verified working — step 1
Two sides and the included angle at P: Area = (12)(PQ)(PR) sin(RPQ)(a(iii)) shortest distance of P from RQ giving your answer to 2 decimal places.[2]
Verified working — step 1
The shortest distance is the perpendicular height h from P onto RQ.(b) Solve the equation 3 tan θ = 89 for 0° ≤ θ ≤ 180°.[1]
Verified working — step 1
Divide first: tan θ = 893 = 29.667(c) Simplify 9x2 - 19x + 3.[2]
Verified working — step 1
9x2 - 1 is a difference of two squares: (3x - 1)(3x + 1).The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.
Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.
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