Notice that the given right triangle is also an isosceles triangle: both acute angles must have a measure of 45º for the internal angles of the triangle to add up to 180º.
Then, the lengths of x and y are the same, since they are opposite to congruent angles.
Additionally, in a right isosceles triangle, the length of the hypotenuse is always √2 times the length of a leg:
Since the length of the hypotenuse of the given triangle is 19√2, then the length of the legs x and y must be 19.
Therefore, the answers are:
x=19
y=19
