Q20 of 47 Page 1

From the top of a 7 m high building, the angle of elevation of the top of a tower is 60° and the angle of depression of its foot is 45°. Find the height of the tower.

Given, height of building = 7 m

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Angle of elevation = ∠EAD = 60°


Angle of depression = ∠EAC = ∠ACB = 45°


Let AB be the building and CD be the tower.


Consider ΔABC,


⇒ tan45° = AB/BC


⇒ 1 = 7/BC


∴ BC = AE = 7 m


Consider ΔAED,


⇒ tan60° = DE/AE


⇒ √3 = DE/7


∴ DE = 7 √3 m


∴ Height of the tower = DE + EC = 7 √3 + 7 = 7 (1 + √3) m


Ans. Height of tower is 7 (1 + √3) m.


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