Krishna
0

Step 1:  Analyse the given information and Draw a figure.

            GIVEN: The pole height AB = 9 m

                          

                  Height of the electric pole to do repair = AB - BC = 9 - 1.8 = 7.2

                  Angle between the ladder and the ground = 60\degree


                    Length of the ladder = ?

                The distance between the foot the  ladder and foot of the pole AD = ?


Step 2: Find the length of the ladder by using the trigonometric ratios

            NOTE: From right triangle ADC,  we know the opposite side and we have to calculate the hypotenuse.  

                             So take the \sin \theta = \frac{opposite}{hypotenuse}  

       

            EXAMPLE:      \sin 60\degree = \frac{AC}{DC}

                                           \frac{\sqrt{3}}{2} = \frac{7.2}{DC}           ( \because \sin 60\degree = \frac{\sqrt{3}}{2}   )


                                         DC = \frac{2*7.2}{\sqrt{3}}

                                Simplify the above equation by Rationalizing


                                        DC = \frac{2*7.2}{\sqrt{3}} \frac{\sqrt{3}}{\sqrt{3}}


                                       DC = \frac{14.4*\sqrt{3}}{3}


                                      DC = 4.8 * 1.732

                                       DC = 8.3136 m

                        Height of the ladder = 8.3136 m


Step 3: Calculate the  distance between the foot the  ladder and foot of the pole by using the trigonometric ratios.

            NOTE: From right triangle ADC,  we know the opposite side and we have to calculate the adjacent side.  

              So take the \tan \theta = \frac{opposite}{hypotenuse}


                EXAMPLE:   \tan 60\degree = \frac{AC}{AD}           

             

                                            \sqrt{3} = \frac{7.2}{AD}


                                            AD = \frac{7.2}{\sqrt{3}}

                    Simplify the above equation by Rationalizing


                                            AD = \frac{7.2}{\sqrt{3}} \frac{\sqrt{3}}{\sqrt{3}}


                                             AD = \frac{7.2*\sqrt{3}}{3}


                                           AD = \frac{7.2*1.732}{3}

                                          AD = 2.4 * 1.732

                                          AD = 4.1568 m

              The  distance between the foot the ladder and foot of the pole = 4.1568 m