Question

Consider a triangle $ABC$ and let $a,b,$ and $c$ denote the lenths of the sides opposite to vertices $A,B$ and $C$ respectively. Suppose $a=6,b=10$ and the area of the triangle is $15\sqrt{3}$. If $\angle ACB$ is obtuse and if $r$ dentoes the radius of the incricle of the triangle, then $r^2$ is equal to\

Answer 1

$\sin C=\frac{\sqrt{3}}{2}$ and $C$ is given to be obtuse.
$\Rightarrow C=\frac{2\pi }{3}$