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Question
The angles of elevation and depression of the top and the bottom of a tower from the top of a building, 60 m high, are 30° and 60° respectively. Find the difference between the heights of the building and the tower and the distance between them.
Solution
Let AB be the building and CD be the tower.
In right ∆ABD:
`(AB)/(BD)=tan 60^@`
`⇒ 60/(BD)=sqrt3`
`⇒ BD=60/sqrt3`
`⇒ BD=20sqrt3`
In right ∆ACE:
`(CE)/(AE)=tan 30^@`
`⇒ (CE)/(BD)=1/sqrt3 (∵AE=BD)`
`⇒CE=(20sqrt3)/sqrt3=20`
Height of the tower = CE + ED = CE + AB = 20 m + 60 m = 80 m
Difference between the heights of the tower and the building = 80 m − 60 m = 20 m
Distance between the tower and the building = BD = `20sqrt3`
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