Krishna
1

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

        

              

            

Richard Daniel
0
Nice