Question

An electric pole is $10m$ 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 ${45}^o$ with the horizontal through the foot of the pole, find the length of the wire.

Answer 1

Consider

$AB$ as the pole and $AC$ as the wire that makes ${45}^o$ with the ground.

And $AC=x$

Given

Height of the pole $AB=10m$,

In right triangle $ABC$

$\sin \theta =\frac{AB}{AC}$

Substituting the values,

$\Rightarrow \sin {45}^o=\frac{10}{x}$

$\Rightarrow \frac{1}{\sqrt{2}}=\frac{10}{x}$

By cross multiplication,

$\Rightarrow x=10\sqrt{2}=10\left(1.414\right)$

$\Rightarrow x=14.14$

Hence, the length of the wire is $14.14m$.