Answer: Choice A)
x = 11*sqrt(2)/2
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Work Shown:
You can use the sine rule to find the value of x
sin(angle) = opposite/hypotenuse
sin(45) = x/11
x = 11*sin(45)
x = 11*sqrt(2)/2
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Or you could use the 45-45-90 triangle template
hypotenuse = sqrt(2)*short leg
11 = sqrt(2)*x
x = 11/sqrt(2)
x = 11*sqrt(2)/2 after rationalizing the denominator
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Or you could use the pythagorean theorem
For a 45-45-90 triangle, the legs are the same length. They are both x for now.
a^2+b^2 = c^2
x^2+x^2 = 11^2
2x^2 = 121
x^2 = 121/2
x = sqrt(121/2)
x = sqrt(121)/sqrt(2)
x = 11/sqrt(2)
x = 11*sqrt(2)/2