JEE Main 2018 (Offline)Question 1
$PQR$ 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:
Trigonometric Ratio & Identities
Solution
Concept. $PQ=PR$, so the line from $P$ to the midpoint $M$ of $QR$ is perpendicular to $QR$. Formulas used. (1) $\text{distance}=h\cot(\text{elevation})$; PythagorasStep 1 - Distances. By (1), $PM=h$ and $QM=h\sqrt3$. Step 2 - Pythagoras. $PQ^2=PM^2+QM^2$: $h^2+3h^2=200^2$, so $h=100$. Answer: (B)