Use the Pythagorean theorem:
[tex]x^2+8^2=16^2\\\\x^2+64=256\qquad\text{subtract 64 from both sides}\\\\x^2=192\to x=\sqrt{192}\\\\x=\sqrt{64\cdot3}\\\\x=\sqrt{64}\cdot\sqrt3\\\\\boxed{x=8\sqrt3\ in}[/tex]
[tex]x^2+5^2=(\sqrt{122})^2\\\\x^2+25=122\qquad\text{subtract 25 from both sides}\\\\x^2=97\to \boxed{x=\sqrt{97}\ in}[/tex]
