Question

An aircraft is flying along a horizontal line PQ directly towards the observer A on the ground and maintaining an altitude of 4500 m, the angles of depression of A from P and Q are 30 degree and 60 degree respectively. Find PQ.

Answer 1

$In\Delta AQT$, $tan{60}^{\circ }=\frac{QT}{AT}$ = $\frac{4500}{AT}$
$AT=\frac{4500}{\sqrt{3}}\dots \dots \left(1\right)$
$\Delta APR,tan{30}^{\circ }=\frac{PR}{AR}$
$\frac{1}{\sqrt{3}}=\frac{4500}{AR}$
$AR=\frac{4500}{\sqrt{3}}$
$QP=AR-AT=4500(\sqrt{3}-\frac{1}{\sqrt{3}})m$
$=4500\left(\frac{2}{\sqrt{3}}\right)m$