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?
How far from the base of the pole should the stake be driven so that the wire will be taut?
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Let AC be a guy wire attached to be a pole AB of height $18\ m$.
Let BC be the distance that the stake is away from the pole so that the wire will be taut.
In $\triangle\text{ABC},$
By Pythagoras Theorem,
$AC^2 = AB^2 + BC^2$
$\Rightarrow 24^2 = 18^2 + BC^2$
$\Rightarrow BC^2 = 24^2 - 18^2$
$\Rightarrow BC^2 = 576 - 324$
$\Rightarrow BC^2 = 252$
$\Rightarrow\text{BC}^2=6\sqrt{7}\text{m}$
So, the stake should be $6\sqrt{7}\text{m}$ away from the pole so that the wire will be taut.
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