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 $6\sqrt7\ m$.

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Updated on: 10-Oct-2022

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