Question

A wire attached to a vertical pole of height 20 m is 29 m long and has a stake attached to its 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 AB be the pole and AC be the wire.
From Pythagoras theorem,
$A{C}^2=A{B}^2+B{C}^2$
$\Rightarrow {29}^2={20}^2+B{C}^2$
$\Rightarrow B{C}^2=841-400$
$\Rightarrow B{C}^2=441$
$\Rightarrow BC=21m$
Therefore, the distance from the base should be $21m$.