Question

$PQR$ is a triangular park with $PQ=PR=200$ m.
A T.V. tower stands at the mid-point of $QR$. If the angles of elevation of the top of the tower at $P,Q$ and $R$ are respectively ${45}^{\circ },{30}^{\circ }$ and ${30}^{\circ }$, then the height of the tower (in m) is:

• A. $50\sqrt{2}$
• B. $50$
• C. $100$
• D. $100\sqrt{3}$

Answer 1

The correct option is C $100$

Let $ST=h$ (height of tower)
From figure it is clear that
In $△STP,$ we have
$\tan {45}^{\circ }=\frac{ST}{PT}$
$PT=ST=h$
In $△STQ,$ we have
$\tan {30}^{\circ }=\frac{ST}{QT}$
$\Rightarrow QT=h\sqrt{3}$
Now, in $△PTQ,$ we have
$P{T}^2+Q{T}^2={200}^2$
$\Rightarrow 4h^2={200}^2$
$\therefore h=100$ m