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 $45 °$ . What is the distance between the base of the tower and the point $P$ ?

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12 units

9 units

$3 \sqrt{3}$ units

data inadequate

answer is C.

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Detailed Solution

$\tan 45 ° = \frac{S R}{Q R}$

$1 = \frac{S R}{Q R} \Rightarrow S R = Q R \to (1)$

$\tan 30 ° = \frac{S R}{P R} = \frac{S R}{P Q + Q R} \to (2)$

From (1) and (2)

Two equations and 3 variables

Hence we can not find the required value with the given data.

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