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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Trignometry
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In $\Delta ABC$ $a=3,b=5,c=6$ find the value of $\sin\large\frac{A}{2}$

$(a)\;\sqrt{14}\qquad(b)\;\large\frac{1}{\sqrt {14}}$$\qquad(c)\;\sqrt{15}\qquad(d)\;\large\frac{1}{\sqrt{15}}$

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1 Answer

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Given : $a=3,b=5,c=6$
We know that
$\sin\large\frac{A}{2}=\sqrt{\large\frac{(s-b)(s-c)}{bc}}$
$s=\large\frac{a+b+c}{2}$
$s=\large\frac{3+5+6}{2}$
$\;\;\;=7$
$\sin\large\frac{A}{2}=\sqrt{\large\frac{(7-5)(7-6)}{5.6}}$
$\quad\quad\;\;=\sqrt{\large\frac{2\times 1}{30}}$
$\quad\quad\;\;=\sqrt{\large\frac{2}{30}}$
$\quad\quad\;\;=\sqrt{\large\frac{1}{15}}$
$\quad\quad\;\;=\large\frac{1}{\sqrt{15}}$
Hence (d) is the correct answer.
answered Oct 10, 2013 by sreemathi.v
 

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