$\begin{array}{1 1}(a)\;\large\frac{\pi}{6}&(b)\;\large\frac{\pi}{3}\\(c)\;\large\frac{\pi}{4}&(d)\;\large\frac{\pi}{5}\end{array}$

Let $a=7cm$

$b=4\sqrt 3$

$c=\sqrt{13}$cm

$\Rightarrow$ Smallest side is C

Smallest angle will be C

$\cos C=\large\frac{a^2+b^2-c^2}{2ab}$

$\qquad=\large\frac{(7)^2+(4\sqrt 3)^2-(\sqrt{13})^2}{2\times 7\times 4\sqrt 3}$

$\qquad=\large\frac{49+48-13}{56\sqrt 3}$

$\qquad=\large\frac{97-13}{56\sqrt 3}$

$\qquad=\large\frac{\sqrt 3}{2}$

$C=\large\frac{\pi}{6}$

Hence (a) is the correct option.

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