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Question
A vertical pole and a vertical tower are on the same level ground in such a way that from the top of the pole, the angle of elevation of the top of the tower is 60o and the angle of depression of the bottom of the tower is 30o. Find: the height of the pole, if the height of the tower is 75 m.
Solution
Let AB be the tower and CD be the pole.
Then ∠ ACE = 60° and ∠ BCE = 30°
Let height of the pole be x m
∴ CD=Be=x
In Δ BEC,
`(BE)/(EC)=tan 30° `
⇒ `EC=sqrt3 x`
`In Δ (AE)/(EC)=tan 60°`
`⇒ (75-x)/(EC)= sqrt3`
⇒ 75-x=3x
`∴ x=75/4=18.75 m`
∴ height of the pole is 18.75m.
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