If the angles of elevation of a tower from two points distant a and (a > b) from its foot and in the same straight line from it are 30° and 60°, then the height of the tower is



Given BC = a and BD = b
Let the height AB = h
In right ΔABD,


tan θ =


tan 30° =



……………1


In Δ ABC


tan 60° =


√3 a = h………………2


Multiplying 1 and 2


h2 = b × √ 3 a


h = √ab

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