Step 1: Analyse the given information and draw a figure based up on the given data.

Height of electric pole AB = h say

Length of the wire AC = 18 m

Wire angle of elevation with the ground = 30 \degree

Wire was cut and tied at an angle of elevation = 60 \degree

Length of the remaining wire after cutting = AD

Step 2: Use the appropriate trigonometric ratios to calculate how much length of the wire was cut.

Length of the wire was cut = AC - AD

We know AC = 18 m

Determine the height of the pole

From the right triangle ACB

\sin 30\degree = \frac{AB}{AC} = \frac{h}{18}

\frac{1}{2} = \frac{h}{18} ( \because \sin 30\degree =\frac{1}{2})

h = \frac{18}{2}

h = 9 m

Determine length of the remaining wire (AD)

From the right triangle ADB

\sin 60\degree = \frac{AB}{AD} = \frac{h}{AD}

\frac{\sqrt{3}}{2} = \frac{h}{AD} ( \because \sin 60\degree =\frac{\sqrt{3}}{2})

AD = \frac{2*9}{\sqrt{3}} ( \because h = 9 m)

Simplify the equation by performing the Rationalization

AD = \frac{18}{\sqrt{3}} * \frac{\sqrt{3}}{\sqrt{3}}

AD = \frac{18 \sqrt{3}}{3}

AD = 6 \sqrt{3}

Length of the wire was cut = AC - AD

= 18 - 6 \sqrt{3}

= 18 - 6 * 1.732

= 18 - 10.392

= 7.608 m