A) \[\frac{\sqrt{3}}{2}\]
B) \[\frac{1}{2}\]
C) \[\frac{1}{\sqrt{2}}\]
D) \[-\frac{1}{\sqrt{2}}\]
E) \[-\frac{1}{2}\]
Correct Answer: C
Solution :
Given that\[a=15,\text{ }b=36,\text{ }c=39\] \[\sin \frac{C}{2}=\frac{\sqrt{(s-a)(s-b)}}{ab}\]and \[s=\frac{a+b+c}{2}\] \[=\frac{15+36+39}{2}=45\] \[\Rightarrow \] \[s-a=30,s-b=9\] \[\therefore \] \[\sin \frac{C}{2}=\sqrt{\frac{30\times 9}{15\times 36}}=\frac{1}{\sqrt{2}}\]
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