# 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 ?

## Solution :

Let AB = 24 m be guy wire attached to a vertical pole BC of height 18 m. To keep the wire taut, let it be fixed to stake at A. Then, ABC is a right angled triangle at C.

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

So, $${24}^2$$ = $${AC}^2$$ + $${18}^2$$

$$\implies$$ $${AC}^2$$ = 576 – 324

$$\implies$$  $${AC}^2$$ = 252

$$\implies$$  AC = $$6\sqrt{7}$$

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