First, to find z, we must first find y. Since y is the altitude, we can use triangle altitude theorem to solve that.
ie. altitude/left side = right side/altitude
[tex]\frac{1}{y} =\frac{y}{8}[/tex]
Cross multiply and you get:
[tex]8=y^{2}[/tex]
[tex]2\sqrt{2} = y[/tex]
Now that we have y, we can solve for z. We can do that using the pythagoream theorem.
[tex]a^2+b^2=c^2[/tex]
[tex](2\sqrt{2})^2 + 8^2 = z^2[/tex]
[tex]8+64=z^2[/tex]
[tex]72 = z^2[/tex]
[tex]6\sqrt{2} = z[/tex]
So z is 6 radical 2
