ECZ 2017 · O-Level Paper 2 · Question 7 — Trigonometry
The diagram 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 degrees.
(a(i)) The diagram shows the houses of a Headman (H), his Secretary (S) and a Trustee (T), where H is 1.3 km from S, T is 1.9 km from H and angle THS = 130 degrees. Calculate the area of triangle THS.[2]
Verified working — step 1
Area = (12)(TH)(HS) sin(angle at H)(a(ii)) Calculate the distance TS.[5]
Verified working — step 1
By the cosine rule:(a(iii)) Calculate 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 degrees which satisfies the equation cos(theta) = 23.[1]
Verified working — step 1
theta = arccos(23) = arccos(0.6667) = 48.19, so theta = …(c) Simplify 2x^2 - 8x + 2.[2]
Verified working — step 1
2x2 - 8 = 2(x2 - 4) = …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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