A) 5
B) \[5\sqrt{3}\]
C) 10
D) None of these
Correct Answer: B
Solution :
Given, in\[\Delta ABC,\text{ }\angle A=30{}^\circ ,\text{ }c=10,\text{ }\angle C=90{}^\circ \] \[\therefore \]\[\angle B=180{}^\circ -(30{}^\circ -90{}^\circ )=60{}^\circ \] Now, \[\frac{b}{\sin B}=\frac{c}{\sin C}\] \[\Rightarrow \] \[\frac{b}{\sin 60{}^\circ }=\frac{c}{\sin 90{}^\circ }\] \[\Rightarrow \] \[\frac{b}{\sqrt{3}/2}=\frac{10}{1}\] \[\Rightarrow \] \[b=10\times \frac{\sqrt{3}}{2}\] \[\Rightarrow \] \[b=5\sqrt{3}\]
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