Question

24. The base of a 13-foot ladder stands 5 feet from a house. Sketch a drawing to model this situation. How many feet up the side of the house does the ladder reach? Explain how drawing the picture helped you solve the problem.

Answer 1

The draw that describes this situation looks like this:

Drawing this helped us to know that the ladder forms a right triangle with one of the walls of the house.

When we have right triangles we can apply the Pythagoras theorem, from the Pythagoras theorem we can express:

`13^2=5^2+h^2`

Solving for h, we get:

`\begin{gathered} 13^2-5^2=5^2-5^2+h^2 \\ 13^2-5^2=h^2 \\ h=\sqrt[]{13^2-5^2}=\sqrt[]{169-25}=\sqrt[]{144}=12 \end{gathered}`

Then, the ladder reach 12 feet up the side of the house