Q12 of 22 Page 9

From a point P on the ground the angle of elevation of the top of a tower is 30° and that of the top of a flag staff fixed on the top of the tower, is 60°. If the length of the flag staff is 5 cm, find the height of the tower.(CBSE 2015)

Image

The figure demonstrates the condition given in the question.


We have to find the distance between D and C.


In Δ BCD,


( tan θ = Height/Base)
⇒


⇒ y = x√3 m ………….(1)


In Δ ABC,


( tan θ = Height/Base)


⇒


⇒ 5 + x = y√3


⇒ 5 + x = (x√3)(√3) (From eq 1)


⇒ 5 + x = 3x


⇒ 2x = 5


⇒ x = 2.5m


∴ Height of tower = x = 2.5m

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