ECZ 2022 · GCE Paper 2 · Question 8 — Trigonometry
Question from ECZ 2022 · GCE Paper 2 · Question 8
(a) In the diagram, XY = 6 cm, angle YXZ = 60° and angle XYZ = 80°. Calculate the
(a(i)) length of YZ,[4]
Verified working — step 1
The third angle: angle Z = 180 - 60 - 80 = 40°.(a(ii)) area of triangle XYZ,[2]
Verified working — step 1
Two sides and the included angle at Y: Area = (12)(XY)(YZ) sin(Y)(a(iii)) shortest distance from X to YZ.[2]
Verified working — step 1
The shortest distance is the perpendicular height h from X onto YZ.(b) Solve the equation tan θ = 2.75 for 0° ≤ θ ≤ 360°.[2]
Verified working — step 1
tan θ = 2.75, related acute angle 70.0°.(c) Simplify 1 - 4x21 + 2x.[2]
Verified working — step 1
1 - 4x2 is a difference of two squares: (1 - 2x)(1 + 2x).The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.
Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.
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