ECZ 2019 · O-Level Paper 2 · Question 12 — Trigonometry

The diagram shows a triangle KMN in which KM = 8 km, MN = 10 km and angle KMN = 92 degrees.

(a(i)) The diagram shows triangle KMN in which KM = 8 km, MN = 10 km and angle KMN = 92 degrees. Calculate KN.[5]

Verified working — step 1

By the cosine rule:

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

Verified working — step 1

Area = (12)(KM)(MN) sin(KMN)

(a(iii)) Calculate the shortest distance from M to KN.[2]

Verified working — step 1

The shortest distance is the perpendicular height h from M to KN.

(b) Solve the equation 2 tan(theta) = -3 for 0 <= theta <= 180 degrees.[1]

Verified working — step 1

tan(theta) = -1.5

(c) Simplify 25p^47q^2divided by 5p^621q^4multiplied by p15q.[2]

Verified working — step 1

Dividing means multiplying 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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