ECZ 2011 · O-Level Paper 2 · Question 11 — Trigonometry
Question from ECZ 2011 · O-Level Paper 2 · Question 11
(a) Three candidates A, B and C took part in a student's union presidential elections. Candidate A received 12 600 votes and candidates B and C followed each other respectively.
(a(i)) Given that the ratio of the votes of candidate A to that of Candidate B is 3:2, calculate the number of votes received by Candidate B,[2]
Verified working — step 1
A : B = 3 : 2, so B is two thirds of A.(a(ii)) Given also that candidate B received 600 more votes than candidate C, calculate the number of votes for candidate C.[2]
Verified working — step 1
B received 600 MORE than C, so C is 600 fewer.(b) A Girls' High School has been built in such a way that the Administration block (A), dormitories (B) and classes (C) are connected by straight corridors. A is 60 m from C and 130 m from B. The bearing of B from A is 110° and the bearing of A from C is 030° as shown below.
(b(i)) Find angle BAC.[1]
Verified working — step 1
The bearing of A from C is 030, so the reverse bearing of C from A is 030 + 180 = 210.(b(ii)) Calculate the distance BC.[5]
Verified working — step 1
Two sides and the included angle: cosine rule.(b(iii)) The Administration decided to build a tuckshop at a point T along BC such that T is the shortest distance from A. Given that the area of triangle ABC is 3 840.75 m2, calculate AT.[2]
Verified working — step 1
AT is the perpendicular height from A to BC.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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