An electric pole is 10 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° with the horizontal through the foot of the pole, find the length of the wire.

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11.11 m

12.12 m

13.13 m

14.14 m

answer is D.

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Detailed Solution

Let AC be the wire of length h and C be the point, making an angle = 45°.

In $∆ A B C$ ,

sin 45° = $\frac{A B}{A C}$

$\Rightarrow$ $\frac{1}{\sqrt{2}}$ = $\frac{10 m}{A C}$

$\Rightarrow$ AC = 10 $\sqrt{2}$ m

$\Rightarrow$ AC = 14.14 m [Taking $\sqrt{2}$ = 1.414]

$∴$ the length of the wire = 14.14 m.

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