A) \[45{}^\circ \]
B) \[60{}^\circ \]
C) \[90{}^\circ \]
D) \[180{}^\circ \]
Correct Answer: A
Solution :
[a] \[\mu =\frac{\sin \frac{{{\delta }_{m}}+A}{2}}{\sin \frac{A}{2}}\] \[\Rightarrow \] \[\sqrt{2}=\frac{\sin \frac{{{\delta }_{m}}+60}{2}}{\sin \,30{}^\circ }\] \[\sin \frac{{{\delta }_{m}}+60}{2}=\sqrt{2}\times \frac{1}{2}=\frac{1}{\sqrt{2}}=\sin \,45{}^\circ \] \[\frac{{{\delta }_{m}}+60}{2}=45{}^\circ \] \[\Rightarrow \]\[{{\delta }_{m}}+60=90{}^\circ ;\] \[{{\delta }_{m}}=30{}^\circ \] Now \[{{\delta }_{m}}=2i-A\] \[\Rightarrow \] \[i=\frac{{{\delta }_{m}}+A}{2}=\frac{30+60}{2}45{}^\circ \]
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