NECO 2001 Mathematics · Question 17

From the top of a storey-buliding, the angle of depression of a mango on a tree 20m away from the base of the…

Question

From the top of a storey-buliding, the angle of depression of a mango on a tree 20m away from the base of the storey building is 68°. if the mango is 4.5 m above the ground, what is the height of the storey building to the nearest metre?

A.55m
B.54m
C.50m
D.49m
E.45m

Answer: B. 54m

Explanation written with AI and checked against the answer key

Analyze the question: From the top of a building, the angle of depression to a mango is 68°. The mango is 20 m horizontally from the base and 4.5 m above the ground. We need the building's height. Concept: The angle of depression from the top equals the angle of elevation from the mango to the top (alternate angles). So in the right-angled triangle formed: tan 68° = (vertical height above the mango) / (horizontal distance) Solution: Let h be the height of the building. The vertical side of the triangle is (h − 4.5). tan 68° = (h − 4.5) / 20 From tables, tan 68° ≈ 2.475 h − 4.5 = 20 × 2.475 = 49.5 h = 49.5 + 4.5 = 54 m Answer: The height of the building is 54 m, which is option B. Tip: In depression/elevation problems, draw the horizontal line from the observer, and subtract or add the height of the object's position carefully. Here the triangle's vertical side starts at the mango's level, not the ground, so you must add 4.5 m at the end. Forgetting this gives 49.5 ≈ 50 m (option C), which is a common trap.

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