Q23 of 47 Page 1

The angles of elevation and depression of the top and the bottom of a tower from the top 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 them.


Let AB be the building = 60 m


And CE be the tower = h m


So, difference between the heights of the building and the tower = DE


And the distance between them = BC


Consider right angled ΔABC,


⇒ tan60° = AB/BC


⇒ √3 = 60/BC


⇒ BC = 60/√3


Rationalizing the denominator,


⇒ BC = 60(√3)/√3(√3)


= 60√3/3


∴ BC = 20√3 m = 20(1.73) = 34.6 m


BC = AD


Consider right angled ΔADE,


⇒ tan30° = DE/AD


⇒ 1/√3 = DE/20√3


⇒ DE = 20√3 / √3


∴ DE = 20 m


Ans. The difference between the heights of the building and the tower DE is 20 m and the distance between them BC is 34.6 m.


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