There is a small island in the river which is 100 \( m \) wide and a tall tree stands on the isl...

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There is a small island in the river which is 100 \( m \) wide and a tall tree stands on the island. \( P \) and \( Q \) are points directly opposite each other on the two banks and in line with the tree. If the angles of elevation of the top of the from \( P \) and \( Q \) are respectively are \( 30^{\circ} \) and \( 45^{\circ} \), find the height of the tree (in metres).
(a) \( 50(\sqrt{3}-1) \)
(b) \( 50(\sqrt{3}+1) \)
(c) \( 100(\sqrt{3}+1) \)
(d) \( 100(\sqrt{3}-1) \)
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