From a point P on the ground the angle of elevation of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flag-staff from P is 45°. Find the length of the flag-staff and the distance of the building from the point P. (Take 
).
Let the height of the flag-staff = h (m)
And the distance of point P from foot of building = 
(m)
In ∆APB,
tan 45° = 
tan 45° =
1 = =
h+10 = 
-------(1)
In ∆DPB,
tan 30° = 
= 
⇒17.32 m. -----------(2)
On substituting value of 
in eqn. (1)
h = 
h = 17.32-10 ⇒ 7.32 m.
Therefore height of flag-staff is 7.32 m. and distance of point P from tower is 17.32 m.
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