![Side of apartment building with 6 section cat ladder attached to the side leading to an apartment balcony](https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/121/2016/08/17161656/Screen-Shot-2016-08-17-at-9.16.31-AM-223x300.png)
Cat heaven
At the beginning of this lesson, we left Joan and her brother who were planning to make a ramp for Joan’s cat Hobbes from her window. She used the Pythagorean Theorem to get this far, but was left with an equation she did not know how to solve:
[latex]\begin{array}{ccc}\hfill {a}^{2}+{b}^{2}& =& {c}^{2}\hfill \\ \hfill {5}^{2}+{12}^{2}& =& {c}^{2}\hfill \\ \hfill 169& =& {c}^{2}\hfill \end{array}[/latex]
The goal was to find the unknown length in the following triangle, where c represents the length of the cat ladder.
![A right triangle with a base of 5 feet, a height of 12 feet, and a hypotenuse labeled c](https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/924/2015/09/25200219/CNX_CAT_Figure_01_03_001.jpg)
Joan’s brother, Jacob, suggested that she use a square root to find the solution to her equation. Joan remembered that roots and exponents are related – one “undoes” the other. She tried it out in the following way:
[latex]\begin{array}{ccc}169 ={c}^{2}\\\sqrt{169}=\sqrt{c^2}\\13=c\end{array}[/latex]
Hooray! Joan has the length she needs to create her cat’s ladder. Hopefully she will be able to get some sleep now.