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Question
The angles of elevation and depression of the top and bottom of a light-house from the top of a 60 m high building are 30° and 60° respectively. Find (i) the difference between the heights of the light-house and the building. (ii) the distance between the light-house and the building.
Solution
Let AB be the building and CD be the light house.
Suppose the height of the light house be h m.
Given: AB = 60 m, ∠EAD = 30° and ∠CAE = 60°.
CE = AB = 60 m
∴ DE = CD − CE = (h − 60) m
In ΔEAD,
In ΔACE,
From (1) and (2), we get
∴ Difference between the height of light house and building = CD − AB = 80 m − 60 m = 20 m
Distance between the light house and building = BC = AE
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