The angles of depression of two ships from an aeroplane flying at the height of $7500 m$ are $30 °$ and $45 ° .$ If both the ships are in the same line and on the same side of the aeroplane such that one ship is exactly behind the other, then the distance between the ships is:

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5475 m

5470 m

5465 m

5460 m

answer is A.

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Detailed Solution

Given,
Height of the aeroplane from the two ships = 7500m
The angles of depression of two ships from an aeroplane are

30 °

and

45 ° .

Consider the figure,
Question Image

The distance between ships is,

x = 7500 tan 30 ° − 7500 tan 45 ° ⇒ x = 75003 − 7500 ⇒ x = 7500 (3 − 1) ⇒ x = 5475 m

Thus, the distance between the ships is 5475 m.
Therefore, option 1 is correct.

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