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A man standing on the deck of a ship, which is $10 m$ above water level, observes the angle of elevation of the top of a hill as $60 °$ and the angle of depression of the base of hill as $30 °$ , then find the height of the hill.

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40 m

10 m

20 m

30 m

answer is A.

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Detailed Solution

Given, level of water=10m
Angle of elevation of the top of a hill is

60 °

.
And angle of depression of the base of hill is

30 °

.
Consider the figure,
Question Image

Let X be the distance between the ship and the hill Determine the distance between hill and ship,

tan 30 ° = height of the deck distance between the ship ⇒ tan 30 ° = 10 X ⇒ X = 10 tan 30 ° ⇒ X = 103 m ∵ tan 30 ° = 13

Let the height of the hill is H,

H = h + 10 ⇒ H = x tan 60 ° + 10 ⇒ H = 103 × 3 + 10 ⇒ H = 40

Distance between hill and ship is

103 m

.
Therefore,
Height of the hill is 40 m.
Therefore, option 1 is correct.

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