ECZ 2020 · O-Level Paper 2 · Question 10 — Trigonometry
Question from ECZ 2020 · O-Level Paper 2 · Question 10
(a) Three villages A, B and C are joined by straight roads as shown in the diagram below. Given that AB = 10.2 km, BC = 15.6 km and AC = 9.4 km, calculate
(a(i)) angle BAC to the nearest whole number,[5]
Verified working — step 1
All three sides known, so cosine rule for the angle at A:(a(ii)) the area of triangle ABC,[2]
Verified working — step 1
Two sides and the included angle at A: Area = (12)(AB)(AC) sin(BAC)(a(iii)) the shortest distance from A to BC.[2]
Verified working — step 1
The shortest distance is the perpendicular height h from A onto BC.(b) Solve the equation 2 cos θ = 1 for 0° ≤ θ ≤ 180°.[1]
Verified working — step 1
cos θ = 12(c) Simplify 3x2 y8xy3 ÷ 9x34y4.[2]
Verified working — step 1
Multiply by the 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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