ECZ 2015 · GCE Paper 2 · Question 7 — Trigonometry

Question from ECZ 2015 · GCE Paper 2 · Question 7

(a) The diagram below shows a triangular garden OAB where OA = 1.7 m, AB = 1.1 m and angle OAB = 114°. Calculate

(a(i)) the area of triangle OAB correct to 1 decimal place,[3]

Verified working — step 1

Two sides OA and AB enclose the angle at A, so use the area rule.

(a(ii)) the distance OB,[5]

Verified working — step 1

Two sides and the included angle at A: cosine rule.

(a(iii)) the shortest distance from A to OB.[2]

Verified working — step 1

The shortest distance h is the perpendicular from A to OB.

(b) A rectangular maize field has a length of 1.5 km and a width of 1.1 km. Calculate the length of its diagonal.[2]

Verified working — step 1

The diagonal, length and width form a right-angled triangle.

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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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