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Question
A man on the deck of a ship, 16m above water level, observe that that angle of elevation and depression respectively of the top and bottom of a cliff are 60° and 30° . Calculate the distance of the cliff from the ship and height of the cliff.
Solution
Let AB be the deck of the ship above the water level and DE be the cliff.
Now,
AB = 16msuch that CD = 16mand ∠BDA = 30° and ∠EBC = 60°
If AD = xmand DE = hm, then CE = (h-16)m.
In the right ΔBAD,we have
`(AB)/(AD) = tan 30° = 1/ sqrt(3)`
`⇒16/x = 1/ sqrt(3)`
` ⇒x = 16 sqrt(3)=27.68m`
In the right ΔEBC,we have:
`(EC)/(BC) = tan 60^0 = sqrt(3)`
`⇒((h-16))/x = sqrt(3)`
`⇒ h - 16 = xsqrt(3)`
`⇒ h - 16=16 sqrt(3) xx sqrt(3) = 48 [ ∵ x = 16 sqrt(3)]`
`⇒ h = 48+16 = 64 m`
∴ Distance of the cliff from the deck of the ship = AD = x = 27.68m
And,
Height of the cliff = DE = h =64m
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