Answer:
12
Explanation:
SOH CAH TOA reminds you that ...
Sin = Opposite/Hypotenuse
so ...
sin(45°) = (6√2)/x
Your memory of trig functions tells you sin(45°) = 1/√2, so we have ...
1/√2 = (6√2)/x
Multiplying by (√2)x gives ...
x = 6(√2)^2 = 6·2
x = 12
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You can simply recognize that this is an isosceles right triangle, so the hypotenuse (x) is √2 times the leg length:
x = (6√2)·√2 = 6·2 = 12