Question

1. The top of a ladder is placed against the side of a house. The ladder is 14 feet long and the wall is 12 feet high. How far from the wall will the base of the ladder be positioned if the top of the ladder meets the top of the wall? (TEKS: 8.7C-R)

Answer 1

We would start by sketching a diagram of what the question described. This is shown below;

The ladder is shown as line AC (resting on the wall).

The wall is shown as line AB.

The distance from the wall to the base of the ladder will be line BC.

Line BC would be calculated using the Pythagoras' theorem as follows;

`\begin{gathered} AC^2=AB^2+BC^2 \\ AC^2-AB^2=BC^2 \\ 14^2-12^2=BC^2 \\ 196-144=BC^2 \\ 52=BC^2 \\ \sqrt[]{52}=BC \\ 7.211102\ldots=BC \\ BC\approx7.2ft \end{gathered}`

The base of the ladder will be 7.2 feet from the wall.