ECZ 2015 · O-Level Paper 2 · Question 10 — Trigonometry

Question from ECZ 2015 · O-Level Paper 2 · Question 10

(a) In Votani Constituency, A, B and C are polling stations as shown on the diagram below. Calculate

(a(i)) angle BAC,[5]

Verified working — step 1

Three sides known, so use the cosine rule for the angle.

(a(ii)) angle ACB,[1]

Verified working — step 1

cos ACB = 43² + 37² - 43²2 × 43 × 37 = 3786 = 0.4302.

(a(iii)) the area of triangle ABC correct to 1 decimal place,[2]

Verified working — step 1

AB = AC = 43, so the perpendicular from A meets BC at its midpoint, 18.5 km along.

(a(iv)) the shortest distance from C to AB.[2]

Verified working — step 1

The shortest distance is the perpendicular from C to AB.

(b) Solve the equation 3(t - 5) - 2 = -1 + t.[2]

Verified working — step 1

Expand: 3t - 15 - 2 = -1 + t.

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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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