The shadow of a vertical tower on level ground increases by $10\;cm$ The attitude of sun changes from the angle of elevation $45 ^{\circ}$ to $30^{circ}$ The height of the tower is _______

Question

$\begin{array}{1 1}(A) \; \large\frac{5}{\sqrt 3 +1} \\(B)\; \large\frac{5}{\sqrt 3 -1} \\(C)\;5(\sqrt 3 -1) \\(D)\;5 (\sqrt 3 +1) \end{array}$