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(C) Let the height of the lighthouse be $h$ and the position of the lighthouse be $O$. Let the two ships be at points $A$ and $B$ on opposite sides.Gi

Vedclass · Accepted Answer

$600$

Vedclass · Answer

(C) Let the height of the lighthouse be $h$ and the position of the lighthouse be $O$. Let the two ships be at points $A$ and $B$ on opposite sides.Given,the distance of the ship with angle of depression $60^{\circ}$ is $150\,m$. Thus,$OA = 150\,m$.In the right-angled triangle formed by the lighthouse and ship $A$,$	an(60^{\circ}) = \frac{h}{150}$.Since $	an(60^{\circ}) = \sqrt{3}$,we have $h = 150\sqrt{3}\,m$.Now,for the second ship at $B$ with angle of depression $30^{\circ}$,$	an(30^{\circ}) = \frac{h}{OB}$.Since $	an(30^{\circ}) = \frac{1}{\sqrt{3}}$,we have $OB = h\sqrt{3} = (150\sqrt{3}) 	imes \sqrt{3} = 150 	imes 3 = 450\,m$.The total distance between the two ships is $OA + OB = 150 + 450 = 600\,m$.

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