Q. 74.4( 21 Votes )
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)
tan 45° =
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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