A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2ft per second. Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 7 feet from the wall.

My Set Up:

tan(theta) = 7/x

Is that the correct trig equation?

I took the implicit derivative of both sides but ended up with a

sec^2 (theta) function that led to the wrong answer.

The book does not explain how to find angles in terms of related rates. How is this done? I will then use your steps to solve similar questions. Thank you.