Here is the problem I'm working on:

A ladder 20ft long leans against a house. If the foot of the ladder is moving away from the house at the rate of 2ft/s, find how fast the slope of the ladder is decreasing when the foot of the ladder is 12ft from the house.

Here is what I have so far:

Given:

- x=12
- z=20
Find:

- when x = 12
My Work:

- By the theorem of Pythagoras:

- y=16
- =

Any tips on where I went wrong?

The book, however, came up with

Thanks in advance!