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 ${45}^{\circ }$ with the horizontal through the foot of the pole, find the length of the wire.

Answer 1

Let AB be the pole of height 10 m and wire AC is tied which makes an angle of 45° with horizontal.

In ΔABC,

$sin45=\frac{AB}{AC}$

$\frac{1}{\sqrt{2}}=\frac{AB}{AC}$

$\frac{1}{\sqrt{2}}=\frac{10}{AC}$

$AC=10\sqrt{2}$

∴ The length of the wire is $10\sqrt{2}$ m.