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

The diagram shows a triangular piece of land ABC in which AB = 1 km, BC = 2.5 km and AC = 2.8 km.

(a(i)) The diagram shows a triangular piece of land ABC with AB = 1 km, BC = 2.5 km and AC = 2.8 km. Calculate angle ABC.[5]

Verified working — step 1

By the cosine rule:

(a(ii)) Calculate the area of triangle ABC.[2]

Verified working — step 1

Area = (12)(AB)(BC) sin(ABC)

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

Verified working — step 1

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

(b) Solve the equation 2 cos(theta) = -1 for 180 <= theta <= 360 degrees.[1]

Verified working — step 1

cos(theta) = -12, and the related acute angle is 60 degrees.

(c) Simplify 42xyz56multiplied by 32xy40x^2 y.[2]

Verified working — step 1

Numbers: 4256= 34and 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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