College Algebra, Chapter 1, 1.3, Section 1.3, Problem 102

A $\displaystyle 19 \frac{1}{2}$ foot ladder leans against a building. The base of the ladder is $\displaystyle 7 \frac{1}{2} ft$ from the building. How high up the building does the ladder reach?









By using Pythagorean Theorem,


$
\begin{equation}
\begin{aligned}

\left( 7 \frac{1}{2} \right)^2 + h^2 =& \left( 19 \frac{1}{2} \right)^2
&&
\\
\\
\left( \frac{15}{2} \right)^2 + h^2 =& \left( \frac{39}{2} \right)^2
&&
\\
\\
\frac{225}{4} + h^2 =& \frac{1521}{4}
&& \text{Subtract } \frac{225}{4}
\\
\\
h^2 =& \frac{1521}{4} - \frac{225}{4}
&&
\\
\\
h^2 =& 324
&& \text{Take the square root}
\\
\\
h =& \pm \sqrt{324}
&& \text{Solve for } h
\\
\\
h =& 18 \text{ and } h = -18
&& \text{Choose } h > 0
\\
\\
h =& 18 ft
&&


\end{aligned}
\end{equation}
$