ECZ 2017 · O-Level Paper 2 · Question 7 — Trigonometry
Question from ECZ 2017 · O-Level Paper 2 · Question 7
(a) The diagram below shows the location of houses for a village Headman (H), his Secretary (S) and a Trustee (T). H is 1.3 km from S, T is 1.9 km from H and angle THS = 130°. Calculate
(a(i)) the area of triangle THS,[2]
Verified working — step 1
Two sides TH and HS enclose the angle at H, so use the area rule.(a(ii)) the distance TS,[5]
Verified working — step 1
Two sides and the included angle: cosine rule.(a(iii)) the shortest distance from H to TS.[2]
Verified working — step 1
The shortest distance is the perpendicular height h from H to TS.(b) Find the angle between 0° and 90° which satisfies the equation cos θ = 23.[1]
Verified working — step 1
cos θ = 23 = 0.6667.(c) Simplify 2x2 - 8x + 2.[2]
Verified working — step 1
Factor the numerator: 2x2 - 8 = 2(x2 - 4) = 2(x - 2)(x + 2).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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