What is the minimum length ladder that a worker needs to access a landing nine feet above the adjacent floor?

12 feet  

So with the standard terms, the ladder should be at least 1 unit away for 4 feet of height so keeping in mind, use the unitary method:

Height                Away from base

4                                   1

9                                    x

Cross multiply:

x = 9/4  

x = 2.5 feet away from the base

Using the Pythagoras Theorem:  

a² + b² = c²  

place the values for the right triangle (a = 2.5, b = 9):  

2.5² + 9² = c²  

= 9.34 feet  

Now, the length is always more than the height so:  

9.34 + 2 = 11.34  

A minimum of 11.34 feet. So rounding off would result in a 12 foot ladder.