Question

A 21-foot ladder is placed against a vertical wall of a building, with the bottom of the ladderstanding on level ground 16 feet from the base of the building. How highup the wall does the ladder reach?The ladder reachesfeet up the wall.

Answer 1

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:

`\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}=√(185)\\ \\ \text{ Wall }=13.6 \end{gathered}`

The height of the wall is 13.6 feet.