\( A B \) is a vertical pole with \( B \) ground level and \( A \) at the top. A man finds that ....

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\( A B \) is a vertical pole with \( B \) ground level and \( A \) at the top. A man finds that the angle of elevation of
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point \( A \) from a certain point \( C \) on the ground is \( 60^{\circ} \). He moves away from the pole along the line \( B C \) to a point \( D \) such that \( C D=8 \mathrm{~m} \). From \( D \), the angle of elevation of point \( A \) is \( 45^{\circ} \). Then the height of the pole is
(1) \( 4 \sqrt{3}(\sqrt{3}-1) \mathrm{m} \)
(2) \( 4 \sqrt{3}(\sqrt{3}+1) \mathrm{m} \)
(3) \( 8 \sqrt{3}(\sqrt{3}-1) \mathrm{m} \)
(4) \( 8 \sqrt{3}(2-\sqrt{3}) \mathrm{m} \)



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