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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 degree with the man’s eye. The man walks some distance towards the tower to watch its top and the angle of elevation becomes 60 degree. What is the distance the base of the tower and the point P?

a. 4√3 units
b. 8 units
c. 12 units

Solution:

The information already given in the question is,

Angle BPA = 30º
Angle BP’A = 60º

The pole or the height of the pole indicated in this figure is BA. Let’s assume BA to be ‘k’.

At first the man was standing at the point P forming the angle of 30º and the when the man moved from the point P to point P’, the angle with respect to the pole became 60º.

The question is to derive the value of AP

The distance between the base of the tower and the point P cannot be calculated as the distance between the top of the tower and point P is not given, the height of the tower is also not mentioned as well as the distance of PP’ is not given in the problem.

All these information were required for calculating AP. Due to the inadequacy of three variables, solution cannot be derived.

Therefore, the correct option for this problem is Option D, Data inadequate.

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