Answer in Brief
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.
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Solution
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.
In ∆ABC,
`tan 30°= h/x`
`⇒ 1/sqrt3=h/x`
`⇒ x= h sqrt3` ................(1)
In ∆BGD,
`tan 60°=(BD)/(GD)`
`⇒ sqrt3=( h+4)/x`
`⇒ x=( h+4)/sqrt3` ................(2)
From (i) and (ii) we get,
`h sqrt3=( h+4)/sqrt3`
`⇒ 3h = h+4`
`⇒2h=4`
`⇒h=2`
Hence, the height of the ballon above the ground = 2 + 4 + 2 = 8 m
Concept: Heights and Distances
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