Question

An electric pole is $10$ m high. A steel wire tied to the top of the pole is affixed at a point on the ground to keep the pole upright. If the wire makes an angle of $45°$ with the horizontal through the foot of the pole, find the length of the wire.

Answer 1

Draw a rough diagram and find the length of the wire :

Given,

Height of the electric pole $\text{'}\mathrm{AB}\text{'}=10\mathrm{m}$

The angle made by steel wire with the ground (horizontal)$\theta =45°$

Let the length of the wire $=AC$

In right-angled triangle ABC.

$\begin{array}{l}\sin 45°=\frac{\mathrm{AB}}{\mathrm{AC}}\\ \Rightarrow \frac{1}{\sqrt{2}}=\frac{10}{AC}\\ \Rightarrow \mathrm{AC}=10\sqrt{2} \mathrm{m}\end{array}$

Hence the length of the wire is$10\sqrt{2} \mathrm{m}$.