ECZ 2016 · GCE Paper 2 · Question 7 — Bearings

Towns L, M, P: M on bearing 060° from L, P on bearing 105° from M; M is 450km from L and 600km from P. Circle centre O, chord AB perpendicular to OC, OC = 4.3cm, AB = 38.2cm.

(a(i)) Calculate the distance between L and P.[5]

Verified working — step 1

Bearing M to L = 060° + 180° = 240°; bearing M to P = 105°.

(a(ii)) Calculate the area of triangle LMP.[3]

Verified working — step 1

Area = ½ · LM · MP · sin(LMP) = …

(a(iii)) Calculate angle MPL.[2]

Verified working — step 1

Sine rule: sinMPLLM= sinLMPLP

(b) Circle centre O, chord AB perpendicular to OC, OC = 4.3cm, AB = 38.2cm. Calculate the radius.[2]

Verified working — step 1

Since OC ⊥ AB, C is the midpoint of AB, so AC = 38.22= 19.1 cm.

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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