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A man on the deck of a ship, 12 m above water level. observes that the angle of elevation of the top of a cliff is $60 °$ and the angle of depression of the base of the cliff is $30 °$ . Find the distance of the cliff from the ship and the height of the cliff. [Use $3 = 1.732$ ]

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50 m

51 m

48 m

49 m

answer is A.

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Detailed Solution

Given that A man on the deck of a ship, 12 m above water level. observes that the angle of elevation of the top of a cliff is

60 °

and the angle of depression of the base of the cliff is

30 °

.
We have to find the distance of the cliff from the ship and the height of the cliff.
In a right-angle triangle,

tan θ = Opposite side Hypotenuse

a man on the deck of a ship is 12m above the water level he observes that the angle of - Maths - Some Applications of Trigonometry - 1473385 | Meritnation.com

Let AB be the deck of the ship. AB=12 cm.
Suppose CE be the cliff. C and E are the top and bottom of the cliff.
Let CE = h m.
Given,

∠ E A D = 60 o a n d ∠ D A C = 30 o .

CD = AB = 12 m.

∴ D E = C E − C D = h − 12 m .

I n △ A D E,

tan 60 o = D E A D ∴ 3 = h − 12 m A D ⇒ A D = h − 12 3 m ⇒ A D = h − 12 3 3 m I n △ A D C, tan 30 o = C D A D ∴ 13 = 12 m A D ⇒ A D = 123 m

Now,

⇒ h − 12 3 3 m = 123 m ⇒ h − 12 = 36 ⇒ h = 36 + 12 ⇒ h = 48

Therefore, the height of the cliff is 48 m and the distance of cliff from the ship = BC = AD =

123 m .

Therefore, the correct option is 1.

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