In the middle of a \( 100 \mathrm{~m} \) wide river, there is a small island and a tall tree sta...

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In the middle of a \( 100 \mathrm{~m} \) wide river, there is a small island and a tall tree stands on that island. \( \mathrm{M} \) and \( \mathrm{N} \) are points which are directly opposite to each other on two banks and in line with the tree. If the angles of elevation of the top of the tree from \( \mathrm{M} \) and \( \mathrm{N} \) are \( 30^{\circ} \) and \( 45^{\circ} \) respectively, find the height of the tree.
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