Question

Date: . A 20-foot wire is tied from the top of a flagpole to a stake in the ground. If the stake is 7 feet from the base of the flagpole, find the height of the flagpole.

Answer 1

First, draw a diagram to show the situation:

Notice that a right triangle is formed. Let h be the height of the flagpole, measured in ft. From the Pythagorean Theorem, we know that:

`h^2+7^2=20^2`

Solve for h:

`\begin{gathered} \Rightarrow h^2+49=400 \\ \Rightarrow h^2=400-49 \\ \Rightarrow h^2=351 \\ \Rightarrow h=\sqrt[]{351} \\ \Rightarrow h=3\cdot\sqrt[]{39} \\ \Rightarrow h\approx18.735 \end{gathered}`

Therefore, the height of the flagpole is:

`\begin{gathered} 3\cdot\sqrt[]{39}\text{ ft} \\ \approx18.735\text{ ft} \end{gathered}`