Question

In a $△ABC,a=5,b=4andtan\frac{C}{2}=\sqrt{\frac{7}{8}}$. The side c is

• A. 6
• B. 3
• C. 2
• D. None of these

Answer 1

The correct option is A

6

$ta{n}^2\frac{c}{2}=\frac{(s-a)(s-b)}{s(s-c)}$
=$\frac{(9+c-10)(9+c-8)}{(9+c)(9-c)}=\frac{c^2-1}{81-c^2}$
$\frac{7}{8}=\frac{c^2-1}{81-c^2}\Rightarrow c=6$