ECZ 2021 · O-Level Paper 2 · Question 12 — Trigonometry

The diagram shows triangle ABC in which AB = 11.5 m, BC = 7.2 m and AC = 15.1 m.

(a(i)) The diagram shows triangle ABC in which AB = 11.5 m, BC = 7.2 m and AC = 15.1 m. 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 15 tan(theta) = 14 for 180 <= theta <= 270 degrees.[1]

Verified working — step 1

tan(theta) = 1415= 0.9333

(c) Simplify 39x^328y^4divided by 65x^556y^5.[2]

Verified working — step 1

Multiply by the reciprocal:

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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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