A man walking due north,observes that the elevation of a balloon which is due east of him and is sailing towards the northwest is then 60 degree.After he walks 400m the balloon is vertically over his head,find the height of the balloon supposing at the same height.

Answer :

Let elevation point of man  =  A  , And after he covers he reached at point B , as now balloon vertically over his head .

Height of balloon  BC  =  h  m 

So,

AB  =  400 m


So,

tan 60$°$ =  $\frac{Oppostite}{Adjacent} = \frac{BC}{AB} = \frac{h}{400}$ , So

$\sqrt{3}$  = $\frac{h}{400}$   ( As we know tan 60$°$ = $\sqrt{3}$  )

h  =  400 $\sqrt{3}$  m

or

h  =  400 $\times$ 1.732  ( As we know $\sqrt{3}$  = 1.732 )

h  = 692.8 m

So,

Height of balloon  =  692.8  m  ( Ans )