Two ships are there in the …
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Two ships are there in the sea on either side of a light house in such a way that the ships and the lighthouse are in the same straight line. The angles of depression of two ships as observed from the top of the lighthouse are 60° and 45°If the height of the lighthouse is 200m, what is the distance between the two ships?
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Sia ? 6 years, 6 months ago
Let PM be the light house of height 200 m and let A and B be two ships on the either sides of lighthouse such that the angles of depression of A and B are {tex}60^o{/tex} and {tex}45^o{/tex} respectively.
Let, AM = x m and BM=y m
Then, {tex}\angle XPB=\angle MBP=45^o{/tex} [alternate angle]
and {tex}\angle YPA=\angle MAP=60^o{/tex} [alternate angles]
In right-angled {tex}\triangle AMP,{/tex} {tex}\tan{60^o}=\frac{P}{B}=\frac{PM}{AM}{/tex}
{tex}\Rightarrow \sqrt3=\frac{200}{x}{/tex}
{tex}\Rightarrow x=\frac{200}{\sqrt3}\;m{/tex}
In right-angled {tex}\triangle BMP, {/tex} {tex}\tan{45^o}=\frac{PM}{BM}{/tex}
{tex}\Rightarrow 1=\frac{200}{y}{/tex}
{tex}\Rightarrow y=200 \;m{/tex}
Now, distance between the two ships = AB = {tex}x+y=200+\frac{200}{\sqrt3}=315.48\;m{/tex}
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