Q26 of 31 Page 1

From a point on the ground, the angles of elevation of the bottom and top of a tower fixed at the top of a 20 m high building are 45o & 60o respectively. Find the height of the tower.


Let BC be a building, AB be the tower on building and D is the point of observation.


Given,


Height of building, BC = 20 m


Angle of elevation to top, θ1 = ∠ADC = 60°


Angle of elevation to bottom, θ2 = ∠BDC = 45°


Let height of tower, AB = h


In ΔBDC





⇒ CD = 20 m


In ΔADC





⇒ AB + BC = 20√3


⇒ h + 20 = 20√3


⇒ h = 20(√3 – 1) meters


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