Question

5(a). A boy stands at a point M on the same horizontal level as the foot, T, of a vertical building. He observes an object on the top, P, of the building at an angle of elevation of 66°. He moves directly backwards to a new point C and observes the same object at an angle of elevation of 53°. If |MT|=50m, illustrate the information in a diagram.
5(b). Calculate, correct to one decimal place, the: (i) height of the building |PT|; (ii) |MC|.

Accepted Answer

(a) The diagram shows a right triangle with T at the base of the building, P at the top, M at 50m from T with angle of elevation 66°, and C further back with angle of elevation 53°.
(b)(i) tan66°=|PT|/50 → |PT|=50×tan66°≈112.3 m.
(ii) tan53°=|PT|/(50+x), where x=|MC|. 112.3=(50+x)×tan53°=(50+x)(1.327) → 112.3=1.327x+66.35 → 1.327x=45.95 → x=34.6m. So |MC|≈34.6 m.

WAEC Mathematics 2023 Theory — Question 5

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