An electric pole is $ 10 \mathrm{~m} $ high. A steel wire tied to top of the pole is affixed at a point on the ground to keep the pole up right. If the wire makes an angle of $ 45^{\circ} $ with the horizontal through the foot of the pole, find the length of the wire.

Given:

An electric pole is \( 10 \mathrm{~m} \) high. A steel wire tied to top of the pole is affixed at a point on the ground to keep the pole up right.

The wire makes an angle of \( 45^{\circ} \) with the horizontal through the foot of the pole.

To do:

We have to find the length of the wire.

Solution:  

Let $AB$ be the electric pole and $AC$ be the length of the steel wire.

From the figure,

$\mathrm{AB}=10 \mathrm{~m}, \angle \mathrm{ACB}=45^{\circ}$

Let the length of the wire be $\mathrm{AC}=h \mathrm{~m}$

We know that,

$\sin \theta=\frac{\text { Perpendicular }}{\text { Hypotenuse }}$

$=\frac{\text { AB }}{AC}$

$\Rightarrow \sin 45^{\circ}=\frac{10}{h}$

$\Rightarrow \frac{1}{\sqrt2}=\frac{10}{h}$

$\Rightarrow h=10 \times \sqrt2 \mathrm{~m}$

$\Rightarrow h=10\sqrt2=10(1.41)=14.1 \mathrm{~m}$

Therefore, the length of the wire is $14.1 \mathrm{~m}$.   

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Updated on: 10-Oct-2022

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