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Question
A man standing on the deck of a ship, which is 8 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 H be the height of hill CE and a man is standing on a ship at the height of 8meter above from the water level.
Let AB = 8, BC = x, AD = BC, AB = DC, DE = h.
∠ACB = 30° and ∠DAE = 60°
We have to find x and H
The corresponding figure is as follows
In ΔABC
`=> tan 30 = 8/x`
`=> 1/sqrt3 = 8/x`
`=> x = 8sqrt3`
Again in Δ DAE,
`=> tan 60^@ = h/x`
`=> sqrt3 = h/x`
`=> h = xsqrt3`
`=> h = 24`
Therefore H = h + 8`
`=> H = 24 + 8`
=> H = 32
Hence the required distance is `8sqrt3`m and height is 32 m
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