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Study Guides > Intermediate Algebra


Side of apartment building with 6 section cat ladder attached to the side leading to an apartment balconyAt the beginning of this lesson, we left Joan and her sister as they 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 didn't know how to solve: [latex-display]\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-display] 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 Joan's sister, Anne, 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-display]\begin{array}{ccc}169 ={c}^{2}\\\sqrt{169}=\sqrt{c^2}\\13=c\end{array}[/latex-display] Hooray!  Joan has the length she needs to create her cat's ladder. Hopefully she will be able to get some sleep now.