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(C) Let $AB$ be the tower of height $100 	ext{ m}$. Let $AC$ and $AD$ be the lengths of the shadows when the angle of elevation is $30^{\circ}$ and $

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$100(\sqrt{3}-1)$

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(C) Let $AB$ be the tower of height $100 	ext{ m}$. Let $AC$ and $AD$ be the lengths of the shadows when the angle of elevation is $30^{\circ}$ and $45^{\circ}$ respectively.In $	riangle ABD$,$	an 45^{\circ} = \frac{AB}{AD} \Rightarrow 1 = \frac{100}{AD} \Rightarrow AD = 100 	ext{ m}$.In $	riangle ABC$,$	an 30^{\circ} = \frac{AB}{AC} \Rightarrow \frac{1}{\sqrt{3}} = \frac{100}{AC} \Rightarrow AC = 100\sqrt{3} 	ext{ m}$.The decrease in the length of the shadow is $x = AC - AD$.$x = 100\sqrt{3} - 100 = 100(\sqrt{3} - 1) 	ext{ m}$.

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 $\text{m}$):

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