The Solution:
Representing the problem in a diagram, we have:
We are asked to find the height of the ladder on the building, that is, length CA.
By the Pythagorean Theorem,
[tex]\begin{gathered} h^2+5^2=15^2 \\ h^2+25=225 \end{gathered}[/tex]
Collecting the like terms, we get
[tex]\begin{gathered} h^2=225-25 \\ h^2=200 \end{gathered}[/tex]
Taking the square root of both sides, we get
[tex]\begin{gathered} \sqrt[]{h^2}\text{ = }\sqrt[]{200} \\ \\ h=10\text{ }\sqrt[]{2}=14.142\approx14.1\text{ feet} \end{gathered}[/tex]
Thus, the ladder will reach 14.1 feet high on the building.
