Question

A guy wire is 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

REF.IMAGE

Let height of vertical pole $AB=18m$ & length of wire $=24m.$

Since the pole is perpendicular to groupd. $\angle ABC={90}^{\circ }$

$\Rightarrow \Delta ABC$ is a right angle triangle.

By pythagoras theorem $A{C}^2=B{C}^2+A{B}^2$

${24}^2=B{C}^2+{18}^2$

$\Rightarrow B{C}^2={24}^2-{18}^2=252$

$\Rightarrow BC=\sqrt{252}=6\sqrt{7}m$

Hence, the stake may be placed at distance

BC = $6\sqrt{7}m.$ from the base of the pole.