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Question
The horizontal distance between two trees of different heights is 60 m. 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 80 m, find the height of the first tree.
Solution
Let the difference between two trees be DE = 60 m and angle of depression of the first tree from the top to the top of the second tree is ∠ABC = 45°.
Let BE = H m, AC = h m, AD = 80m.
We have to find the height of the first tree
The corresponding figure is as follows
In ΔABC
`=> tan B = (AC)/(BC)`
`=> tan 45° = h/60`
`=> 1 - h/60`
`=> h = 60`
Since H = 80 - h
=> H = 80 - 60
=> H = 20
Hence the heght of first tree is 20 m
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