Q. 184.4( 17 Votes )

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.

Answer :

Given that the height of lower window is OR = 2m

Height of upper window is RQ = 4 m

Let height of balloon above the ground is BO = H meter & PO = x meter

Bw2R = 60° and Bw1Q = 30°

In ∆Bw2R,

In ∆Bw1Q,

x = 3 (H - 6) eq. 2

Comparing eq. 1 and eq. 2, we get

H 2 = 3 (H 6)

H 2 = 3H 18

3H H = 18 2

2H = 16

H = 8

Hence, height of the balloon above the ground is 8 meter.

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