Can someone answer this really quick??

 Choice A)

x = 11*sqrt(2)/2

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

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

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