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.

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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