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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 elevation becomes 60°. What is the distance between the base of the tower and the point P?
- 43 units
- 8 units
- 12 units
- Data inadequate
Correct answer: Data inadequate
Solution
Let the tower height be h and the initial distance from P be x. From the first position, tan 30° = h/x, and from the second position, tan 60° = h/(x-d), where d is the distance walked. Since both h and d are unknown, x cannot be uniquely determined. Therefore, the data is inadequate.
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