ECZ 2023 · O-Level Paper 2 · Question 11 — Trigonometry

Question from ECZ 2023 · O-Level Paper 2 · Question 11

(a) In the following triangle, PQ = 41.6 m, PR = 70 m and angle PQR = 105°. Calculate

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

Verified working — step 1

Two sides and a non-included angle, so use the sine rule to find R:

(a(ii)) the area of triangle PQR,[2]

Verified working — step 1

PQ and PR meet at P, so use the angle between them:

(a(iii)) the shortest distance from Q to PR.[2]

Verified working — step 1

The shortest distance is the perpendicular height h from Q onto PR.

(b) Solve the equation tan θ = 2.75 for 180° ≤ θ ≤ 270°.[1]

Verified working — step 1

tan θ = 2.75, related acute angle 70.0°.

(c) Simplify 3d² - 27d + 3.[2]

Verified working — step 1

3d² - 27 = 3(d² - 9) = 3(d - 3)(d + 3)

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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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