Is this triangle similar to a Pythagorean Triple?

The triangle is similar to the Pythagorean Triple $\text{3-4-5}$, with a scale factor of $4$.

The missing side is similar to $4$ on the $\text{3-4-5}$ triangle.
With a scale factor of $4$, the missing side is $4·4=16$ inches.

This is a $45^\circ\text{-}45^\circ\text{-}90^\circ$ triangle. What is the scale factor between this
$45^\circ\text{-}45^\circ\text{-}90^\circ$ special triangle and the given triangle?

With a scale factor of $4$. Missing sides are...

$4$ and $4\sqrt{2}$.

Is this triangle similar to a Pythagorean Triple of $\text{3-4-5}$ or $\text{5-12-13}$?

With a $30^\circ\text{-}60^\circ\text{-}90^\circ$ triangle, the short side is half the length of the hypotenuse so it is $10$.
The side opposite the $60^\circ$ angle is multiplied by the square root of $3$. So it is...

$10\sqrt{3} \text{ m}$