A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60°. What is the distance between the base of the tower and the point P?
Aptitude
Height and Distance
Difficulty: Easy
Choose an option
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A√3 h
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Bh/√3
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C2h
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D3h
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ENone of these
Answer
Correct Answer: √3 h
Explanation
Geometry
- At point P, angle of elevation to the top is 30°; tower height = h.
- Distance of P from the tower's base = x.
Use tangenttan 30° = h / x ⇒ (1/√3) = h / xx = √3 h
The subsequent change to 60° after walking closer is consistent but not needed to find x from the first position.