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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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