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

Answer 1

Answer: (A)

100

Answer 2

Let height of tower $T M$ be $h$ $\therefore P M=h$ In $\Delta T Q M, \tan 30^{\circ}=\frac{h}{Q M}$ $Q M=\sqrt{3} h$ In $\Delta P M Q, \,\,\,\,\, P M^{2}+Q M^{2}=P Q^{2}$ $h^{2}+(\sqrt{3} h)^{2}=200^{2}$ $\Rightarrow 4 h^{2}=200^{2}$ $\Rightarrow h=100\, m$