The angle of depressions of two ships from the top of a light house and on the same side of it are found to be $45 °$ and $30 °$ . If the ships are 200 m upart, then find the height of the light house.

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300 (3 + 1) m

100 (3 + 1) m

50 (3 + 1) m

200 (3 + 1) m

answer is B.

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Detailed Solution

Given that the angle of depressions of two ships from the top of a lighthouse and on the same side of it are found to be

45 °

and

30 °

. The ships are 200m apart.
We have to find the height of the lighthouse.
In a right-angle triangle,

tan θ = Opposite side Adjacent side .

Let D and C be given ships and AB be the lighthouse. Let Height of light house is A B=h In

Δ BAC

, we have:

tan 45 ° = AB BC 1 = A B B C ⇒ A B = B C So, BC = h ...... (1)

In triangle ADB,
Question Image

By rationalization and simplification, we get,

h = 100(3 +1)m

.
The height of the light house is

100 (3 + 1) m .

Therefore, the correct option is 2.

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