Question

4. The diagram shows a tower TR and an observer at O. |OR| = 84 m and the angle of elevation of the top T from O is 57°.
(a) Calculate, correct to three significant figures, the height of the tower.
(b) The observer at O moved away from the tower in the same straight line until the angle of elevation of T is 49°. Find, correct to two decimal places, how far the observer moved backwards.

Accepted Answer

(a) tan 57° = |TR|/84
   |TR| = 84 × tan 57° = 84 × 1.5399 ≈ 129 m

(b) Let x = backward distance
   tan 49° = 129.3516/(x + 84)
   x + 84 = 129.3516/tan 49°
   x + 84 = 112.444
   x = 112.444 − 84 = 28.44 m

WAEC Mathematics 2025 Theory — Question 4

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