This is the isosceles right triangle, the diagonal of a square, the thing that so upset the Pythagoreans. The two sides and diagonal of a square are in ratio [tex]1:1:\sqrt{2}[/tex] so we get
[tex]u = v = 8[/tex]
We could have also gotten this using Trig:
[tex]u = (8 \sqrt{2}) \sin 45^\circ = 8 \sqrt{2}/\sqrt{2} = 8[/tex]
[tex]v = (8\sqrt{2})\cos 45^\circ = 8[/tex]
Or by recognizing u=v because remaining angle is 45 so this must be isosceles so
[tex]u^2 + u^2 = (8 \sqrt{2})^2[/tex]
[tex]2u^2 = 2 (8^2)[/tex]
[tex]u = 8[/tex]
