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,


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