Question

46 Two ships are there in the sea on both side of the light house in such a way that two
ships and the light house are in a 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 light house​

Answer 1

Correct Question:

Two ships are there in the sea on both side of the light house in such a way that two ships and the light house are in a 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 light house is 200 m, find the distance between the two ships.

Given:

✰ AC = 200 m

✰ ∠B = 60°

✰ ∠D = 45°

To find:

✠ The distance between the two ships BD.

Solution:

Let the ships are at B and D and the top of the light house be A as shown in the figure provided in the attachment.

The distance between the two ships,

⟹ BD = BC + CD

In ∆ABC,

➙ tan 60° = AC/BC

➙ √3 = 200/BC [ ∵ tan 60° = √3 ]

➙ BC = 200/√3

➙ BC = 200/1.73 [ taking √3 = 1.73 ]

➙ BC = 115.606

➙ BC = 115.61 m

In ∆ACD,

➙ tan 45° = AC/CD

➙ 1 = 200/CD [ ∵ tan 45° = 1 ]

➙ CD = 200 m

Now,

➤ BD = BC + CD

➤ BD = 115.61 + 200

➤ BD = 351.61 m

∴ The distance between the two ships BD = 351.61 m

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