$A$ 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?

(N/A) Let $OB$ be the pole and $AB$ be the wire. The pole is vertical,so $\triangle AOB$ is a right-angled triangle with $\angle AOB = 90^{\circ}$.
By Pythagoras theorem,
$AB^{2} = OB^{2} + OA^{2}$
$(24\, m)^{2} = (18\, m)^{2} + OA^{2}$
$576\, m^{2} = 324\, m^{2} + OA^{2}$
$OA^{2} = (576 - 324)\, m^{2} = 252\, m^{2}$
$OA = \sqrt{252}\, m = \sqrt{36 \times 7}\, m = 6\sqrt{7}\, m$
Therefore,the distance from the base is $6\sqrt{7}\, m$ (approximately $15.87\, m$).