Geometry help

The right angle at the bottom right sets up the following relationship

4 / y = y / 16     cross-multiply

16 * 4  =  y^2

64  = y^2     take the square root of both sides

8  = y

So....using the Pythagorean Theorem, we have that

z^2  = 4^2 + y^2

z^2  = 16  + 8^2

z^2  =  16  + 64

z^2  = 80       take the square root of both sides

z  = √80

If you want to simplify this :

z  = √ [16 * 5 ]

z = √16   * √5

z = 4√5