Square symmetrical triangles

Let's call the long side of the triangle $c$ ,the longest side of the triangle is:

$a^2+b^2=c^2 \therefore \sqrt{a^2+b^2}=c$

Let's call short side of the square symmetrical triangle $a$ .So, $c$ is:

$c=\sqrt{a^2+a^2}=\sqrt{2a^2}=a\sqrt2$

The ratio of the long side and the short side is :

$\frac{c}{a}=\frac{a\sqrt2}{a}=\sqrt2$

So the angle is:

$\sin^{-1}(\sqrt2)=45^\circ$