For this problem, we are told that a ladder is positioned against a wall, and we need to determine how high on the wall the ladder reaches.
We can create a triangle with the ladder, the wall and the ground such as shown below:
We can determine the height of the wall by using Pythagora's theorem:
[tex]\begin{gathered} \text{ Ladder }^2=\text{ Wall}^2+\text{ Floor}^2\\ \\ 21^2=\text{ Wall}^2+16^2\\ \\ \text{ Wall}^2=441-256\\ \\ \text{ Wall}=\sqrt{185}\\ \\ \text{ Wall }=13.6 \end{gathered}[/tex]The height of the wall is 13.6 feet.
