WAEC Mathematics 2015 Theory — Question 17
Question 17 of 22 from the West African Examinations Council (WAEC) Mathematics 2015 Theory paper, with the correct answer and a full explanation.
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10(b). From an aeroplane in the air at a horizontal distance of 1050m, the angles of depression of the top and base of a control tower at an instance are 36° and 41° respectively. Calculate, correct to the nearest metre: (i) the height of the control tower; (ii) the shortest distance between the aeroplane and the base of the control tower.
Model answer
(i) EB (height above tower top) = tan36°×1050 ≈ 762.67m. EA (height above tower base) = tan41°×1050 ≈ 912.75m. Height of tower = EA−EB ≈ 912.75−762.67 ≈ 150m. (ii) Shortest distance from aeroplane to tower base, EB(hyp) = 1050/cos41° ≈ 1391m.
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