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# Solution - 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 a hill as 30°. Find the distance of the hill from the ship and the height of the hill - CBSE Class 10 - Mathematics

#### Question

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 a hill as 30°. Find the distance of the hill from the ship and the height of the hill

#### Solution

Let CD be the hill and suppose the man is standing on the deck of a ship at point A.

The angle of depression of the base C of the hill CD observed from A is 30° and the angle of elevation of the top D of the hill CD observed from A is 60°.

∴ ∠EAD = 60° and ∠BCA = 30°

In ΔAED,

tan60° = (DE)/(EA)

:.sqrt3=h/x

:.h=sqrt3x

In ABC

tan30° = (AB)/(BC)

:.1/sqrt3=10/x

:.x=10sqrt3

Substituting x =  10 sqrt3 in equation (1) we get

h=sqrt3xx10sqrt3=10xx3=30

∴ DE = 30 m

∴ CD = CE + ED = 10 + 30 = 40 m

Thus, the distance of the hill from the ship is 10sqrt3 m and the height of the hill is 40 m

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#### Reference Material

Solution for question: 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 a hill as 30°. Find the distance of the hill from the ship and the height of the hill concept: Heights and Distances. For the course CBSE
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