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Question
A man is standing on the deck of a ship, which is 10 m above water level. He observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 30°. Calculate the distance of the hill from the ship and the height of the hill.
Solution
Let AB be the height of the hill.
In right-angled ΔBCD,
`"CD"/"DB" = tan 30°`
⇒ DB = 10√3 m.
In right-angled ΔAMC,
`"AM"/"CM" = tan 60°`
⇒ AM = √3 CM
⇒ AM = √3 DB = √3 x 10√3 = 30 m
Thus,
AB = AM + MB
AB = (30 + 10) m = 40 m
∴ Height of the hill be 40 m.
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