The value of x is 8/√2 and y is going to be 8/√2. It is found by using sine and cosine function.
In the given figure we can see that there is a right angle triangle with one is its angle measuring 45 degrees with hypotenuse 8 , base y and perpendicular y.
We need to find the value of x and y .
So , in order to find the value of x sine function
sin(45) = perpendicular / hypotenuse
sin(1/√2) = x / 8
x = 8/√2
So , the value of x is going to be 8/√2.
Now , by using cosine function we can find the value of y too.
cos(45) = base / hypotenuse
cos(1/√2) = y / 8
y = 8/√2.
The value of y is also going to be 8/√2.