ECZ 2020 · O-Level Paper 2 · Question 10 — Trigonometry
Three villages A, B and C are joined by straight roads as shown in the diagram, where AB = 10.2 km, BC = 15.6 km and AC = 9.4 km.
(a(i)) Three villages A, B and C are joined by straight roads, where AB = 10.2 km, BC = 15.6 km and AC = 9.4 km. Calculate angle BAC to the nearest whole number.[5]
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By the cosine rule:(a(ii)) Calculate the area of triangle ABC.[2]
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Area = (12)(AB)(AC) sin(BAC)(a(iii)) Calculate the shortest distance from A to BC.[2]
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The shortest distance is the perpendicular height h from A to BC.(b) Solve the equation 2 cos(theta) = 1 for 0 <= theta <= 180 degrees.[1]
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cos(theta) = …(c) Simplify 3x^2 y8xy^3divided by 9x^34y^4.[2]
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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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