a
\(\text { As } \mu=\frac{\sin \left(\frac{D_{\min }+A}{2}\right)}{\sin \left(\frac{A}{2}\right)}\)

\(\sqrt{2}=\frac{\frac{\sin \left(D_{\min }+60\right)}{2}}{\sin \left(\frac{60}{2}\right)}\)

\(\Rightarrow \frac{1}{\sqrt{2}}=\sin \left(\frac{D_{\min }+60}{2}\right)\)

\(\Rightarrow \frac{D_{\min }+60}{2}=45\)

\(\Rightarrow D_{\min }=30\)