Answer:
x = y = 8
Step-by-step explanation:
We presume you want the values of x and y.
The angle not shown is also 45°, as the two acute angles are complementary. Then the triangle isosceles and x = y.
If you need to, you can use the Pythagorean theorem to find the value of x (and y).
(8√2)² = x² + x²
128 = 2x² . . . . simplify
64 = x² . . . . . . divide by 2
8 = x . . . . . . . . positive square root
The values of x and y are both 8.
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Hopefully, you will memorize the side ratios of an isosceles right triangle. They are ...
1 : 1 : √2
Multiplying these numbers by 8 gives ...
x : y : 8√2 = 8 : 8 : 8√2
In short, recognizing the factor of √2 in the number on the hypotenuse, you know immediately the values of x and y are both 8 in this 45°-45°-90° triangle.
