# 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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