The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window . At certain instant the angles of elevation of a balloon from these windows are observed to be 600 and 300 respectively. Find the height of the balloon above the ground.
Let the window G be 2 m above the ground.
Window A be 4 m above the window G.
Balloon be at point B above the ground.
`tan 30°= h/x`
`⇒ x= h sqrt3` ................(1)
`⇒ sqrt3=( h+4)/x`
`⇒ x=( h+4)/sqrt3` ................(2)
From (i) and (ii) we get,
`h sqrt3=( h+4)/sqrt3`
`⇒ 3h = h+4`
Hence, the height of the ballon above the ground = 2 + 4 + 2 = 8 m