Two ships are there in the sea on either side of a light house in such a way that the ships and the light house are in the same straight line. The angles of depression of two ships as observed from the top of the light house are $60 °$ and $45 °$ . If the height of the light house is $200 m$ , find the distance between the two ships.

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316 m

416 m

516 m

616 m

answer is A.

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Detailed Solution

Given that two ships are there in the sea on either side of a lighthouse 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 ° .

We have to find the distance between the two ships if the height of the lighthouse is 200m.
In a right-angle triangle

tan θ = Opposite side Hypotenuse .

Let d be the distance between the two ships. Suppose the distance of one of the ships from the light house is X meters, then the distance of the other ship from the light house is (d-x) meter.
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