A geometric proof can be achieved by drawing a sketch.

Draw a right-angled triangle, base=x, vertical side=y, hypotenuse=w.

The angle at the lower left corner is 50 degrees, 90 degrees at the lower right,

top angle=40 degrees.

Draw another hypotenuse at 70 degrees from the lower left apex and continue the vertical,

as shown in the attachment.

since w = k, as the top triangle is isosceles.

From Pythagoras' theorem....

therefore....

which is