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  4. A tower PQ stands on a horizontal ground with base Q on the ground. The point R divides the tower in two parts such that QR =15 m. If from a point A on the ground the angle of elevation of R is 60° and the part PR of the tower subtends an angle of 15° at A, then the height of the tower is :

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Q. A tower $PQ$ stands on a horizontal ground with base $Q$ on the ground. The point $R$ divides the tower in two parts such that $QR =15 \,m$. If from a point $A$ on the ground the angle of elevation of $R$ is $60^{\circ}$ and the part $PR$ of the tower subtends an angle of $15^{\circ}$ at $A$, then the height of the tower is :

JEE MainJEE Main 2022Trigonometric Functions

Solution:

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$ \frac{15}{ AQ }=\tan 60^{\circ}$
$\frac{15+x}{ AQ }=\tan 75^{\circ} $
$ \frac{(1)}{(2)} \Rightarrow x=10 \sqrt{3}$So, $P Q=5(2 \sqrt{3}+3) m$