A) \[\frac{7}{2}\]
B) \[7\sqrt{3}\]
C) \[\frac{7}{2}\sqrt{3}\]
D) \[7\sqrt{2}\]
Correct Answer: C
Solution :
Given, in\[\Delta ABC,\angle A=30{}^\circ ,\angle C=90{}^\circ ,c=7\sqrt{3}\] By sine rule\[\frac{a}{\sin A}=\frac{c}{\sin C}\] \[\Rightarrow \] \[a\sin C=c\sin A\] \[\Rightarrow \] \[a\sin 90{}^\circ =7\sqrt{3}\sin 30{}^\circ \] \[\Rightarrow \] \[a=7\sqrt{3}.\frac{1}{2}\] \[\Rightarrow \] \[a=\frac{7}{2}\sqrt{3}\]
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