Question

A guy attached wire to a vertical pole of height $18m$ is $24m$ long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut $?$

Answer 1

Finding the distance from the base of the pole:

($AB$ is a pole$=18m$ , $AC$ is a wire $=24m$)

In right-angled triangle ABC, By Pythagoras' theorem

$$\begin{gathered} \Rightarrow {\left(AC\right)}^2={\left(AB\right)}^2+{\left(BC\right)}^2 \\ \Rightarrow {\left(24\right)}^2={\left(18\right)}^2+{\left(BC\right)}^2 \\ \Rightarrow 576=324+{\left(BC\right)}^2 \\ \Rightarrow {\left(BC\right)}^2=576-324 \\ \Rightarrow {\left(BC\right)}^2=252 \\ \Rightarrow BC=\sqrt{252} \\ \Rightarrow BC=6\sqrt{7} \end{gathered}$$

Therefore, the stake may be placed at a distance of $6\sqrt{7}$ from the base of the pole.