Krishna
0

Step 1: Analyse the give data and construct an imaginary figure by the given hints.

            GIVEN: The angles of elevation of the top of the tower from the two points

                              are complementary angles.

                        Let, if you say angle of elevation \angle ADC = \theta

                          then, angle of elevation \angle ACB = 90\degree - \theta


                        

                      The distance between the pole and points

                                              BC = 4 cm

                                              DB = 9m

                

                  Height of the tower AB = ?


Step 2: Determine the height of the tower by using the trigonometric ratios

                From the figure:

                      Take right angle triangle ADB  

                                       \tan \theta = \frac{opposite}{adjacent} = \frac{AB}{DB}


                                     \tan \theta = \frac{AB}{9}.....................(1)

                  

                    Take right triangle ACD


                         \tan (90\degree - \theta) = \frac{AB}{CB}

                    

                         \cot \theta = \frac{AB}{4}.................(2)        (\because \tan (90\degree - \theta) = \cot \theta )


Step 3: Multiplying equation (1) and (2)

                   \tan \theta = \frac{AB}{9}..................(1)                  

                 \cot \theta = \frac{AB}{4}.................(2)

                Multiply

                   \cot \theta * \tan \theta = \frac{AB}{4} * \frac{AB}{9}


                     \frac{1}{\tan \theta} *\tan \theta = \frac{AB^2}{36}     (\because \cot \theta = \frac{1}{\tan \theta} )


                                       1 = \frac{AB^2}{36}   


                                AB^2 = 36

                             AB = \sqrt{6*6}

                                  AB = 6 m

          The height of the tower = 6 m