Explanation:
remember the trigonometric right-angled triangle inscribed into a norm-circle (radius = 1) ?
sine of the angle at the center of the circle (and the bottom left vertex of the triangle) is the vertical (up/down) leg, cosine is the horizontal (left/right) leg of the triangle.
for us here that means
the 45° angle is at the center of the (imaginary) circle, y is the radius. 7×sqrt(2) is sin(45) multiplied by the radius (y).
x is cos(45) multiplied by the radius (y).
so, we need to start, where we are missing only one variable : sin(45)×y
sin(45)×y = 7×sqrt(2)
y = 7×sqrt(2)/sin(45) = 7×sqrt(2)/sqrt(2)/2 = 14
and we don't need to calculate much for x. for the angle of 45° sine and cosine are equal.
so,
x = 7×sqrt(2)
for any other angle we would have calculated
x = cos(angle)×radius = cos(angle)×14
cos(45) = sqrt(2)/2
x = 14×sqrt(2)/2 = 7×sqrt(2)