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.
Answers
Height of tower = 70 m , Height of Flag staff = 51.24 m
Step-by-step explanation:
Height of tower = H m
Height of Flag staff = F m
Horizontal Distance of observational point from Tower = 70 m
Tan 45° = Height of tower / Horizontal Distance of observational point from Tower
=> 1 = H/70
=> H = 70
=> Height of tower = 70 m
Tan 60° = (Height of tower + Height of Flag staff)/ Horizontal Distance of observational point from Tower
=> √3 = ( 70 + F)/70
=> 70√3 = 70 + F
=> F = 70(√3 - 1)
=> F = 51.24
Height of Flag staff = 51.24 m
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