This is a 45°-45°-90° triangle, in which the sides occur in a ratio of 1 to 1 to √2. So x = √2.
If you didn't already know that, you can trigonometry. By definition of cosine,
cos(45°) = 1/x
Then
x = 1/cos(45°) = 1/(1/√2)) = √2
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