If in a triangle ABC , a = 2 ,   b = 3 and c = 4 , then tan A 2 =

Given,

In a triangle $\mathrm{ABC},a=2, b=3$ and $c=4$,

Now we know that $\tan \left(\frac{A}{2}\right)=\sqrt{\frac{\left(s-b\right)\left(s-c\right)}{s\left(s-a\right)}}$ where $s=\frac{a+b+c}{2}$

Now using the above formula we will find the required value,

So, $s=\frac{2+3+4}{2}=4.5$

Now $\tan \left(\frac{A}{2}\right)=\sqrt{\frac{\left(4.5-3\right)\left(4.5-4\right)}{4.5\left(4.5-2\right)}}$

$\Rightarrow \tan \left(\frac{A}{2}\right)=\sqrt{\frac{1.5\times 0.5}{4.5\times 2.5}}$

$\Rightarrow \tan \left(\frac{A}{2}\right)=\sqrt{\frac{15\times 5}{45\times 25}}$

$\Rightarrow \tan \left(\frac{A}{2}\right)=\sqrt{\frac{1}{15}}$