#1**+1 **

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

CPhill
Apr 3, 2018