a building is made keeping the lower window of the building at a height of 2m above the ground and it's upper window 6m vertically above the lower window in view to have proper sunlight. At a certain instant, the angle of elevation of a balloon from these windows are observed to be 60°and 30°respectively. Find the height of the balloon from the ground.
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according to question
In triangle CAE
Tan 60 = CE/AE
root 3 = CE/AE
Also
In triangle BCD
Tanf 30 = CD/BD
Thus 1/ root 3 = CD/BD
1/root3 = CD/AE
Thus
CE = 3 CD
Also
CE - CD = 6
So CD = 3
thus height of balloon = 3 + 6 + 2
= 11 m
In triangle CAE
Tan 60 = CE/AE
root 3 = CE/AE
Also
In triangle BCD
Tanf 30 = CD/BD
Thus 1/ root 3 = CD/BD
1/root3 = CD/AE
Thus
CE = 3 CD
Also
CE - CD = 6
So CD = 3
thus height of balloon = 3 + 6 + 2
= 11 m
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