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Question
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 60 m high, find the height of the building.
Options
30 m
40 m
20 m
10 m
MCQ
Solution
20 m
Explanation:
The given situation can be represented by figure above
`therefore "tan" 60^circ = "DC"/"BC" => "BC" = "DC"/("tan" 60^circ) = 60/sqrt3 = 20sqrt 3 "m"`
`"tan" 30^circ = "AB"/"BC"`
`=> "AB" = "BC" xx "tan" 30^circ = 20 sqrt3 xx (1/(sqrt3 "m")) = 20 "m"`
Thus, height of building is 20 m.
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