Question

If $a=13,b=12,c=5$ in $△ABC$ where $a,b,c$ are the sides of triangle,

then $\sin \frac{A}{2}=$

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

Answer 1

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

In $\Delta ABC$, we have $a=13,b=12,c=5$

$\Rightarrow \angle A={90}^o$ since it is opposite the greatest side in the triangle and because we have the Pythagoras theorem being followed as ${13}^2={12}^2+5^2$

$\Rightarrow \sin \frac{A}{2}=\sin {45}^o=\frac{1}{\sqrt{2}}$