A tree standing on a horizontal plane is leaning towards east. At two points situated at distanc...

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A tree standing on a horizontal plane is leaning towards east. At two points situated at distances \( a \) and \( b \) exactly due west on it, the angles of elevation of the top are respectively \( \alpha \) and \( \beta \). Prove that the height of the top from the ground is
\[
\frac{(b-a) \tan \alpha \tan \beta}{\tan \alpha-\tan \beta}
\]
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