Question

A guy wire attached 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

First, draw the figure,

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

As we know that according to Pythagoras' theorem$\Rightarrow {\left(H\right)}^2={\left(P\right)}^2+{\left(B\right)}^2$

In right-angled triangle ABC, $\Rightarrow {\left(AC\right)}^2={\left(AB\right)}^2+{\left(BC\right)}^2$

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

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