Question

How far up the wall does the shorter ladder reach?

Answer 1

The setup of both ladders will give us two triangles as shown below:

Since both triangles have 2 equal angles in both triangles, this means that they are both similar.

Hence, we can have a ratio of their sides equal to each other as follows:

`(|AC|)/(|AB|)=(|DF|)/(|DE|)`

Substituting, we have

`\begin{gathered} (25)/(35)=(x)/(14) \\ \therefore \\ x=(25*14)/(35) \\ x=10\text{ ft} \end{gathered}`

The height is 10 feet.