9514 1404 393
Answer:
Step-by-step explanation:
Since this is a right triangle, the acute angles are complementary.
y° = 90° -45°
y° = 45°
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The two acute angles are congruent, so the triangle is isosceles. That is, x = z. The Pythagorean theorem tells you the relation between the sides of the triangle:
x² + z² = (4√2)²
x² +x² = 4²×2 . . . substitute x for z, since they are equal
x² = 4² . . . . . . . divide by 2
x = 4 . . . . . . . . .take the positive square root
z = 4 . . . . . . . . same as x
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Additional comment
Whenever you see a 45° angle in a right triangle you know immediately that it is isosceles, and that the ratios of the side lengths are 1 : 1 : √2. This is one of two "special" triangles that have angles and side ratios that are not difficult to remember.
The hypotenuse here is 4√2, so the other sides are 4.
x : z : 4√2 = 1 : 1 : √2 = 4 : 4 : 4√2
x = z = 4
