Question

A guy wire attached to a vertical pole of height 18 m is 24 m 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

Let AB be a guy wire attached to a pole BC of height 18 m. Now, to keep the wire taut let it to be fixed at A.
Now, In right triangle ABC
By using Pythagoras theorem, we have
$$\begin{gathered} {\mathrm{AB}}^2={\mathrm{BC}}^2+{\mathrm{CA}}^2 \\ \Rightarrow {24}^2={18}^2+{\mathrm{CA}}^2 \\ \Rightarrow {\mathrm{CA}}^2=576-324 \\ \Rightarrow {\mathrm{CA}}^2=252 \\ \Rightarrow \mathrm{CA}=6\sqrt{7}\mathrm{m} \end{gathered}$$
Hence, the stake should be driven $6\sqrt{7}$m far from the base of the pole.