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ICSE / ISC eBooks

Example – 1. The shadow of a vertical tower on a level ground increases by 10 m when the altitude of the sun changes from 45º to 30º. Find the height of the tower, correct to two decimal places.

Solution :-

Fig. – 3.

 Let the height of the tower be h and length of shadow be x meter initially. 

                  In ΔABC,               tan 45º = AB/BC
                                                           1 = h/x
                                                  Or,     h = x

                  In Δ ABD,               tan 30º = AB/DB
                                                         1/√3= h/(x + 10)
                                                      x + 10= h√3
                                                     h + 10 = h√3 
                                               h(√3 – 1) = 10
                                                         h = 10 (√3 + 1)/(√3 – 1)(√3 + 1) 
                                                            = 10 (√3 + 1)/(3 – 1)
                                                            = 10 (√3 + 1)/2
                                                            =  5 (√3 + 1) = 5 (1.732 + 1)
                                                            = 5×2.732 = 13.66 meter.