ECZ 2019 · O-Level Paper 2 · Question 11 — Earth Geometry
Question from ECZ 2019 · O-Level Paper 2 · Question 11
(a) The points P, Q, R and T are on the surface of the earth as shown in the diagram below. [Take π as 3.142 and R = 3437 nm]
(a(i)) Find the difference in longitude between the points T and R.[2]
Verified working — step 1
T (90 W) and R (45 E) sit on opposi…(a(ii)) Find, in nautical miles, the distance between
(a(ii)(a)) P and Q along the latitude 65° N,[2]
Verified working — step 1
P and Q share latitude 65 N with a longitude difference of 135°.(a(ii)(b)) P and T along the longitude 90° W.[2]
Verified working — step 1
P (65 N) and T (55 S) share meridian 90 W, on opposite sides of the equator.(b) The figure below shows a right pyramid with a vertex O and a square base ABCD of side 8 cm. Angle CPD = angle OPC = 90°. Given that OA = OB = OC = OD = 10 cm, calculate
(b(i)) the height OP,[4]
Verified working — step 1
The square base has side 8, so the diagonal AC = 8 √2 and PC = half of that = 4 √2.(b(ii)) the angle between the edge OC and the base PC.[2]
Verified working — step 1
PC is the projection of the edge OC onto the base, so the required angle is 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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