Question

The ladder will reach ___ ft high up on the building.

Answer 1

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,

`\begin{gathered} h^2+5^2=15^2 \\ h^2+25=225 \end{gathered}`

Collecting the like terms, we get

`\begin{gathered} h^2=225-25 \\ h^2=200 \end{gathered}`

Taking the square root of both sides, we get

`\begin{gathered} \sqrt[]{h^2}\text{ = }\sqrt[]{200} \\ \\ h=10\text{ }\sqrt[]{2}=14.142\approx14.1\text{ feet} \end{gathered}`

Thus, the ladder will reach 14.1 feet high on the building.