ECZ 2022 · O-Level Paper 2 · Question 9 — Trigonometry

Question from ECZ 2022 · O-Level Paper 2 · Question 9

(a) The diagram shows a triangular piece of land ABC. Given that AB = 1 km, BC = 2.5 km and AC = 2.8 km, calculate the

(a(i)) angle ABC,[5]

Verified working — step 1

All three sides known, so use the cosine rule for the angle:

(a(ii)) area of triangle ABC,[2]

Verified working — step 1

Two sides and the included angle at B: Area = (12)(AB)(BC) sin(ABC)

(a(iii)) shortest distance from B to AC.[2]

Verified working — step 1

The shortest distance is the perpendicular height h from B onto AC.

(b) Solve the equation 2 cos θ = -1 for 180° ≤ θ ≤ 360°.[1]

Verified working — step 1

cos θ = -12, related acute angle 60°.

(c) Simplify 42xyz56 × 32xy40x² y.[2]

Verified working — step 1

Numbers: 4256 = 34 and 3240 = 45, so (34)(45) = 35.

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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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