Two trees are standing along the opposite sides of a road Distance between the two trees is 400 metr...........

Quantitative Aptitude (CGL) Height and Distance

Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angle of depressions of the point from the top of the trees are 45o and 60o. If the height of the tree which makes 45o angle is 200 metres, then what will be the height (in metres) of the other tree?

20√3

10√3

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Explanation:

Let AB is the building of height x and the shadow of the tree changed from AC to AD where CD = 40m
In ΔABD, tan 600 = AB/AD
⇒ √3 = x/AD ⇒ AD = x/√3
In ΔACB, tan 300 = AB/AC
=>1/√3=x/x/√3+40
⇒ 1/√3 (x/√3 + 40) = x
⇒ x/3 + 40/√3 = x ⇒ 40/√3 = x -x/3
⇒ 40/√3 = 2x/3
⇒ x = (40×3)/2√3 = 20√3m