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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?

Difficulty: Easy

√3 h
h/√3
2h
3h
None of these

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 tangent
tan 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.

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