Question

In $\Delta ABC,$ If $a=13cm,b=12cm,c=5cm,$ then $\sin \frac{A}{2}=$

• A. $\frac{1}{\sqrt{5}}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\sqrt{\frac{32}{35}}$
• D. $\frac{2}{3}$

Answer 1

The correct option is B $\frac{1}{\sqrt{2}}$

Given: $a=13cm,b=12cm,c=5cm,$
$\Rightarrow s=\frac{30}{2}=15cm$
We know,
$\Rightarrow \sin \frac{A}{2}=\sqrt{\frac{(s-b)(s-c)}{bc}}$
$\Rightarrow \sin \frac{A}{2}=\sqrt{\frac{(15-12)(15-5)}{12\times 5}}$
$\Rightarrow \sin \frac{A}{2}=\frac{1}{\sqrt{2}}$