ECZ 2019 · O-Level Paper 2 · Question 11 — Earth Geometry
The points P, Q, R and T are on the surface of the earth as shown in the diagram. (Take pi as 3.142 and R = 3437 nm.)
(a(i)) The points P, Q, R and T are on the surface of the earth as shown in the diagram. Find the difference in longitude between the points T and R.[2]
Verified working — step 1
T lies on longitude 90 degrees W an…(a(ii)(a)) Find, in nautical miles, the distance between P and Q along the latitude 65 degrees N.[2]
Verified working — step 1
P and Q are on latitude 65 degrees N with a difference in longitude of 135 degrees.(a(ii)(b)) Find, in nautical miles, the distance between P and T along the longitude 90 degrees W.[2]
Verified working — step 1
P is at 65 degrees N and T at 55 degrees S on the same meridian, so the difference in latitude is 65 + 55 = 120 degrees.(b(i)) The figure shows a right pyramid with vertex O and a square base ABCD of side 8 cm, where angle CPD = angle OPC = 90 degrees and OA = OB = OC = OD = 10 cm. Calculate the height OP.[4]
Verified working — step 1
For the square base of side 8 cm the diagonal AC = 8 sqrt(2) cm.(b(ii)) Calculate the angle between the edge OC and the base PC.[2]
Verified working — step 1
PC is the projection of OC on the base, so the required angle is angle OCP.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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