Q30 of 52 Page 1

The angles of elevation and depression of the top and bottom of a light-house from the tip 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.


Let AB = 60 m be the building and


CE be the light – house


So,


In right ∆ABC,


Tan 60° = AB/BC


√3 = 60/BC


√3 BC = 60


…(i)


= 20(1.732) = 34.64 m


As we know opposite sides of a triangle are equal,


So here we have;


AD = BC


From (i),


AD = 20√3 ……(ii)


In right ∆ADE,


Tan 30° = DE/AD


1/√3 = DE/20√3


√3 DE = 20√3


DE = 20


Therefore;


(i) Difference between the heights = 20 m and,


(ii) Distance = 34.64 m


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