Krishna
0

Step 1: According to the given data make a figure.

                      


            NOTE: Height of the building AB = DE = h

                        The distance between the building and tower BD = AE = 7 m

                        The angle of elevation of the top of a cell tower = 60 \degree

                        The angle of depression to it's foot = 45 \degree


Step 2: Find the height of the cell tower by using the trigonometric ratios

                      Height of the cell tower DC = CE + ED

                    

                    Determine the length of CE:

                    NOTE: From triangle ACE

                                         \tan 60 \degree = \frac{opposite}{adjacent} = \frac{CE}{AE}


                                                               \tan 60 \degree = \frac{CE}{7}    (Since BD = AE)


                                                                     \sqrt{3} = \frac{CE}{7} ( \because \tan 60 \degree = \sqrt{3} )


                                                                 CE = x = 7 \sqrt{3} ..............(1)


                        Determine the length of ED:

                                From right triangle ABD

                                                       \tan 45\degree = \frac{opposite}{adjacent} = \frac{AB}{BD}


                                                         \tan 45\degree = \frac{AB}{7} (Since, equation (1))


                                                                     1 = \frac{AB}{7} ( \because \tan 45\degree = 1 )


                                                                      AB = 7 

                                                                AB = DE = h = 7 m

              

                          Height of the  tower CD = CE + ED

                                                         CD = 7\sqrt{3} + 7

                                                         CD = 7(\sqrt{3} + 1)

                                                                  CD = 7 (1.732 + 1)

                                                                  CD = 7 (2.732)

                                                                  CD = 19.124 m