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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 angles of depression of the point from the top of the trees are 45° and 60°. If the height of the tree which makes 45° angle is 200 metres, then what will be the height (in metres) of the other tree?

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 angles of depression of the point from the top of the trees are 45° and 60°. If the height of the tree which makes 45° angle is 200 metres, then what will be the height (in metres) of the other tree? Correct Answer 200√3

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In the figure, H is the height of the other tree.

In triangle AEB, AB = 200/tan45°

⇒ AB = 200 mtr

⇒ BC = 400 - 200 = 200 mtr

In triangle DCB, tan 60° = H/BC

⇒ H = 200√3 mtr

∴ Height (in metres) of the other tree = 200√3 mtr

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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 45 degand 60 deg. If the height of the tree which makes 45 degangle is 200 metres, then what will be theheight (in metres) of the other tree?
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