A man standing on a horizontal plane observes the angle of elevation of the top of a tower as $45^\circ$. On walking 40 m towards the tower, the angle of elevation becomes $60^\circ$. Find the height of the tower.
Options:
- A: $\dfrac{40(\sqrt{3}+1)}{2}$ m
- B: $\dfrac{40\sqrt{3}}{\sqrt{3}-1}$ m
- C: $20(3+\sqrt{3})$ m
- D: $40(\sqrt{3}-1)$ m
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