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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?
Given:
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.
To do:
We have to find the distance the stake should be driven so that the wire will be taut.
Solution:
Let AB be the pole and AC be the wire.
This implies,
BC is the distance the stake should be driven so that the wire will be taut.
$AC=24\ m$ and $AB=18\ m$
$\triangle ABC$ is a right-angled triangle. Therefore, by Pythagoras theorem,
$AC^2=AB^2+BC^2$
$(24)^2=(18)^2+BC^2$
$BC^2=576-324$
$BC^2=252\ m^2$
$BC=\sqrt{252}\ m$
$BC=\sqrt{36\times7}\ m$
$BC=6\sqrt7\ m$
Therefore, the distance the stake should be driven so that the wire will be taut is $6\sqrt7\ m$.