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Example – 2. Two people standing on the same side of a tower in a straight line with it, measure the angles of elevation of the top of the tower as 25º and 50º respectively. If the height of the tower is 70 m, find the distance between the two people.

Solution :-

Fig. – 4.

                  Let AB be the tower of height 70 m.
                  In Δ ABC                                 cot 50º = BC/AB
                  Or,                              cot (90º – 40º) = BC/70
                  Or,                                        tan 40º = BC/70
                  Or,                                          BC = 70 tan40º
                                                                   = 70×0.8391
                                                                        = 58.74 m

                  In Δ ABD                                   cot 25º = BD/AB
                    Or,                               cot (90º – 65º) = BD/70
                   Or,                                          tan 65º = BD/70
                   Or,                                           BD = 70 tan 65º
                   Or,                                     BD = 70 × 2.114451
                                                                            = 148.01

                  Hence, distance between two people = CD = BD – BC
                                                                     = 148.01 – 58.74
                                                                                  = 89.27 m.