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Question
The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If height of the tower is 50 m, find the height of the hill.
Solution
Let AB be the tower and CD be the hill
In ΔABD
`tan 30^@ = (AB)/(BD)`
`=> 1/sqrt3 = 50/(BD)`
`=> BD = 50sqrt3`
In ΔCDB
`tan 60^@ = (CD)/(BD)`
`=> sqrt3 = (CD)/(50sqrt3)`
=> CD = 150
Therefore, the height of the hill is 150 m
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