Question

A guy attached a wire 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 height of vertical pole $=AB=18$m

Let the length of wire$AC=24$m

Since the pole will be perpendicular (vertical) to ground

$\angle ABC={90}^{\circ }$

$\Rightarrow △ABC$ is a right-angled triangle.

So, in right-angled triangle $ABC$

Using Pythagoras theorem,

${AC}^2={AB}^2+{BC}^2$

$\Rightarrow {24}^2={18}^2+{BC}^2$

$\Rightarrow {BC}^2=576-324=252$

$\Rightarrow BC=\sqrt{36\times 7}=6\sqrt{7}$m

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