Answer:
x = 2
Explanation:
We'll start with this useful fact about triangles: equal angles in a triangle sweep out equal sides. If a 45 degree angle here sweeps out a length of x, the other one must do the same, so the legs of this right triangle must both be x.
Next, we can use the Pythagorean Theorem to tie all of the triangle's lenghts together:
x² + x² = (√8)²
Finally, we can solve for x:
2x² = 8
x² = 4
x = 2.