From the top of a 45 m high light house, the angles of depression of two ships, on the opposite side of it, are…
CBSE Class 10 Maths PYQ · Applications of Trig · Double Triangle · 5 Marks · March 2024 · Standard
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525 Marks · March 2024 · Standard
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 $30^\circ$ and $60^\circ$. If the line joining the ships passes through the foot of the light house, find the distance between the ships. (Use $\sqrt{3} = 1.73$)
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1 mark for correct figure Let $AB$ be the light house and $C$ and $D$ be positions of ships. $\tan 60^\circ = \sqrt{3} = \frac{45}{y}$ $\Rightarrow y=15\sqrt{3}$ $\tan 30^\circ = \frac{1}{\sqrt{3}} = \frac{45}{x}$ $\Rightarrow x = 45\sqrt{3}$ Distance between two ships $= x+y = 60\sqrt{3}$ $= 60 \times 1.73 = 103.8$ m
