An observer on the top of a cliff,200, m abov | vedclass

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(D) Let the cliff be $PQ = 200\, m$. Let the two ships be at points $R$ and $S$.In $\Delta PQS$,the angle of elevation is $45^{\circ}$.$	an 45^{\circ

Vedclass · Accepted Answer

$146.4$

Vedclass · Answer

(D) Let the cliff be $PQ = 200\, m$. Let the two ships be at points $R$ and $S$.In $\Delta PQS$,the angle of elevation is $45^{\circ}$.$	an 45^{\circ} = \frac{PQ}{QS} = 1$$QS = PQ = 200\, m$.In $\Delta PQR$,the angle of elevation is $30^{\circ}$.$	an 30^{\circ} = \frac{PQ}{QR} = \frac{1}{\sqrt{3}}$$QR = PQ 	imes \sqrt{3} = 200\sqrt{3}\, m$.The distance between the ships is $RS = QR - QS$.$RS = 200\sqrt{3} - 200 = 200(1.732 - 1) = 200(0.732) = 146.4\, m$.

An observer on the top of a cliff,$200\, m$ above the sea level,observes the angle of depression of two ships at anchor to be $45^{\circ}$ and $30^{\circ}$ respectively. Find the distance between the ships,if the line joining them stretches to the base of the cliff. (in $m$)

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