ECZ 2016 · O-Level Paper 2 · Question 10 — Trigonometry
Question from ECZ 2016 · O-Level Paper 2 · Question 10
(a) The diagram below shows the location of three secondary schools, namely Kamubala (K), Belengani (B) and Pendeni (P) in a district. P is 5 km from K, B is 3 km from K and angle PKB = 110°. Calculate
(a(i)) BP,[5]
Verified working — step 1
Two sides and the included angle: cosine rule.(a(ii)) the area of triangle BKP,[2]
Verified working — step 1
Two sides KP and KB enclose the angle at K, so use the area rule.(a(iii)) the shortest distance from K to BP.[2]
Verified working — step 1
The shortest distance is the perpendicular height h from K to BP.(b) Solve the equation tan θ = 0.7 for 0° ≤ θ ≤ 180°.[1]
Verified working — step 1
tan θ = 0.7, so θ = tan-1(0.7) = 34.99°.(c) Simplify 17k220a2 ÷ 51k25a.[2]
Verified working — step 1
Dividing by a fraction means multiplying by its reciprocal.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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