The height of a tower is $100 \text{ m}$. When the angle of elevation of the sun changes from $30^{\circ}$ to $45^{\circ}$,the shadow of the tower becomes $x \text{ m}$ smaller. The value of $x$ is (in $\text{m}$):
- A$100$
- B$100 \sqrt{3}$
- C$100(\sqrt{3}-1)$
- D$\frac{100}{\sqrt{3}}$
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