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

Let $AC=18m$ be the pole.

$BC=24m$ is the length of a guy wire and is attached to stake B.

$\therefore$ In $△ABC$

By pythagoras theorem,

$B{C}^2=A{B}^2+A{C}^2$

$\therefore$ ${24}^2=A{B}^2+{18}^2\Rightarrow A{B}^2=576-324=252$

$\therefore$ $AB=6\sqrt{7}m$

Hence, the stake has to be $6\sqrt{7}m$ from base A.