MCQ
In $\triangle A B C$, if $a=13, b=14$ and $c=15$, then $\sin \left(\frac{A}{2}\right)=$
- A$\frac{1}{5}$
- B$\sqrt{\frac{1}{5}}$
- C$\frac{4}{5}$
- D$\frac{2}{5}$
✓
Answer
(B) $\sqrt{\frac{1}{5}}$
$s=\frac{a+b+c}{2}=\frac{13+14+15}{2}=21$
$\sin \left(\frac{A}{2}\right)=\sqrt{\frac{(s-b)(s-c)}{b c}}=\sqrt{\frac{(21-14)(21-15)}{14 \times 15}}=\sqrt{\frac{1}{5}}$
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