A flag-staff stands on the top of a 5 m high tower. From a point on the ground, the angle of elevation of the top of the flag-staff is 60° and from the same point, the angle of elevation of the top of the tower is 45°. Find the height of the flag-staff.
In the fig let AD is the Flag-Staff of height h (m)
In ∆ABC
tan 45° = 
1 = 
x = 5m
In ∆DBC
tan 60° = 
√3 = 
h + 5 = 5√3
h = 5√3-5
h = 5(√3-1)
h = 3.66 m
Therefore height of flag-staff is 3.66m
66