Write the pythagorean theorem for each one of the 3 right traingles:
[tex]\begin{gathered} 16^2=z^2+x^2 \\ \\ z^2=y^2+4^2 \\ \\ x^2=y^2+12^2 \end{gathered}[/tex]1. Solve x^2 in the first equation:
[tex]x^2=16^2-z^2[/tex]2. Solve y^2 in the second equation:
[tex]y^2=z^2-4^2[/tex]3. Substitute the x^2 and y^2 in the third equation by the values you get in the previous steps:
[tex]16^2-z^2=z^2-4^2+12^2[/tex]4. Solve z^2:
[tex]\begin{gathered} -z^2-z^2=-4^2+12^2-16^2 \\ -2z^2=-16+144-256 \\ -2z^2=-128 \\ z^2=\frac{-128}{-2} \\ \\ z^2=64 \end{gathered}[/tex]5. Use the value of z^2 to solve x and y:
[tex]\begin{gathered} x^2=16^2-z^2 \\ x^2=256-64 \\ x^2=192 \\ x=\sqrt{192} \\ x\approx13.9 \\ \\ \\ y^2=z^2-4^2 \\ y^2=64-16 \\ y^2=48 \\ y=\sqrt{48} \\ y\approx6.9 \end{gathered}[/tex]Then, the values of x and y are:x=13.9y=6.9