spread the spirit of togetherness

Let, $BC=b$ and $AB=a$ .

Now, $a^2+b^2=13^2$ and $(b+17)^2+a^2=24^2$ .

Subtracting first equation from second we get,

$34b+17^2=24^2-13^2$ or, $b=\boxed{3.47}$ .