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A tree breaks due to storm and its top t...

A tree breaks due to storm and its top touches the ground in such a manner that the distance from the top of the tree to the base of the tree and present height are equal. Calculate how much angle is made by the top of the tree with the base.

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Let AB be the tree and it breaks at the point C such that BD = BC, where the top of the tree meets the ground at the point D.
Let `angleBDC = theta`
Now, from the right-angled `DeltaBCD` we get,
`tan theta = (BC)/(BD)` [ by difinition ]
`rArr " " tan theta = (BC)/(BC) " "[because " " BD = BC ("given" )]`
`rArr tan theta = 1 = tan 45^(@) " " rArr theta = 45^(@)`.
Hence the top of the tree makes an angle of `45^(@)` with the base.
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