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Question
The horizontal distance between two trees of different heights is 100m. The angle of depression of the top of the first tree when seen from the top of the second tree is 45°. If the height of the second tree is 150m, find the height of the first tree.
Solution
Let AC and BD be two trees.
BD = 150 m, AE = CD = 100 m
In ΔBAE,
`tan 45^circ = "BE"/"AE"`
⇒ `1 = "BE"/100`
⇒ `"BE" = 100`
∴ AC = BD - BE = 150 m - 100 m = 50 m
Thus, the height of the first tree is 50 m.
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