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Mathematics · 2024 · 5 marks
CBSE 2024 · Region 2 · Set 1 · Q34
From the top of a 45 m high light house, the angles of depression of two ships, on the opposite side of it, are observed to be 30° and 60°. If the…
From the top of a $\displaystyle 45$ m high light house, the angles of depression of two ships, on the opposite side of it, are observed to be $\displaystyle 30$° and $\displaystyle 60$°. If the line joining the ships passes through the foot of the light house, find the distance between the ships. (Use $\displaystyle \sqrt{3}=1.73$ )
Marking-scheme solution
Let AB be the light house and C and D be positions of ships.
\[\begin{aligned}
& \tan 60^{\circ}=\sqrt{3}=\frac{45}{y} \\
& \Rightarrow y=15 \sqrt{3} \\
& \tan 30^{\circ}=\frac{1}{\sqrt{3}}=\frac{45}{x} \\
& \Rightarrow x=45 \sqrt{3}
\end{aligned}
\]
Distance between two ships \(\displaystyle =\mathrm{x}+\mathrm{y}=60 \sqrt{3}\)
\[=60 \times 1.73=103.8 \mathrm{~m}
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