Answer
$1$
Work Step by Step
Notice that $\frac{\pi}{4}$ is equivalent to $45^{\circ}$.
Using the $45-45-90$, the hypotenuse has a length that is $\sqrt 2$ times as long of either of the shorter equal sides.
Let $x$ be the length of shorter equal sides of the triangle $45-45-90$; then by using the definition of tangent:
$$\tan\frac{\pi}{4}=\tan 45^{\circ}=\frac{x}{x}=1$$
