A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff. At a point on the plane 70 metres away from the tower, an observer notices that the angles of elevation of the top and the bottom of the flag-staff are respectively 60° and 45°. Find the height of the flag-staff and that of the tower.

Let the height of tower = h (m)


Let the height of the flag-staff = t (m)


In ∆DBC,


tan 45° =


1 =


h = 70 m


Therefore height of tower = 70m.


Now in ∆ABC,



tan 60° =


√3 = ⇒ √3 = (on substituting value of h =70)


70+t = 70√3


t = 70√3-70


t = 70 (√3 -1)


t = 70 × (1.732-1)


t = 70 × 0.732 ⇒ 51.24 m.


Therefore height of the flag- staff is 51.24 m.


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