JEE Math Practice Question

$$AB$$ is a vertical pole with $$B$$ at the ground level and $$A$$ at the top. $$A$$ man finds that the angle of elevation of the point $$A$$ from a certain point $$C$$ on the ground is $${60^ \circ }$$. He moves away from the pole along the line $$BC$$ to a point $$D$$ such that $$CD=7$$ m. From $$D$$ the angle of elevation of the point $$A$$ is $${45^ \circ }$$. Then the height of the pole is :

1. A.$${{7\sqrt 3 } \over 2} {1 \over {\sqrt {3 - 1} }}m$$
2. B.$${{7\sqrt 3 } \over 2}\left( {\sqrt {3 } + 1 } \right)m$$
3. C.$${{7\sqrt 3 } \over 2}\left( {\sqrt {3 } - 1 } \right)m$$
4. D.$${{7\sqrt 3 } \over 2} {1 \over {\sqrt {3 + 1} }}m$$