Answer
$x=6, h=3\sqrt 3, s=3\sqrt 3, r=3\sqrt 6$
Work Step by Step
$\cos 60^{\circ}=\frac{y}{x}=\frac{3}{x}$
$\implies x=\frac{3}{\cos 60^{\circ}}=\frac{3}{\frac{1}{2}}=6$
$\tan 60^{\circ}=\frac{h}{y}=\frac{h}{3}$
$\implies h=3\tan 60^{\circ}=3\sqrt 3$
The ratio of the lengths of sides in a triangle with angles $45^{\circ},45^{\circ}$ and $90^{\circ}$ is $1:1:\sqrt 2$.
Therefore, in $\triangle ADC$, $DC=AD$ and $AC=\sqrt {2}\times DC$
That is, $h=s=3\sqrt {3}$ and
$r=\sqrt {2}h=\sqrt {2}\times3\sqrt {3}=3\sqrt {6}$
