An electric pole is 10 m high. A steel wire tied to top of the pole is affixed at a point on the ground

Question:

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.

Solution:

Let AC be the wire of length m and C be the point, makes an angle of 45°

In a triangle ABC, given that height of electric pole is BC = 2m and angle C = 45°

Now we have to find the length of wire.

So we use trigonometrically ratios.

In a triangle ABC,

$\Rightarrow \quad \sin C=\frac{A B}{A C}$

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

$\Rightarrow \quad \frac{1}{\sqrt{2}}=\frac{10}{h}$

$\Rightarrow \quad h=10 \sqrt{2}$

Therefore 

Hence the length of wire is  meters.

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