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As observed from the top of a 100m high light house from the sea-level, the angles of depression of two ships are $30 °$ and $45 ° .$ If one ship is exactly behind the other on the same side of the light house, the distance between the two ships is:

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43.2 m

53.2 m

63.2 m

73.2 m

answer is D.

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Detailed Solution

Given,
Height of lighthouse = 100m
The angles of depression of two ships are

30 °

and

45 ° .

Consider the figure,
Question Image

We know,

\tan 45 ° = 1

\tan 30 ° = \frac{1}{\sqrt{3}}

The distance between two ships,

Distance = \frac{100}{\tan 30 °} - \frac{100}{\tan 45 °}

\Rightarrow Distance = 100 \sqrt{3} - 100

\Rightarrow Distance = 100 (\sqrt{3} - 1)

\Rightarrow Distance = 100 (1.732 - 1)

\Rightarrow Distance = 100 (0.732)

\Rightarrow Distance = 73.2

m
Thus, the distance between two ships is 73.2 m.
Therefore, option 4 is correct.

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