Answer
$x=y=\dfrac{\sqrt {42}}{2}$
Work Step by Step
Consider the lengths of the sides of the triangle, $x$ and $y$.
$\sin \theta=\dfrac{Opposite}{Hypotenuse}=\dfrac{y}{h}$
and $\cos \theta=\dfrac{Adjacent}{Hypotenuse}=\dfrac{x}{h}$
Here, $\sin 45^{\circ}=\dfrac{y}{h} \implies \dfrac{1}{\sqrt 2}=\dfrac{y}{\sqrt {21}}$
This gives: $y=\dfrac{\sqrt {42}}{2}$
Now, $\cos 45^{\circ}=\dfrac{x}{h} \implies \dfrac{1}{\sqrt 2}=\dfrac{x}{\sqrt {21}}$
This gives: $x=\dfrac{\sqrt {42}}{2}$
Hence, $x=y=\dfrac{\sqrt {42}}{2}$
