Let C be the base of the mountain AB. AB=3400ft.  D is the point from which the cable is to be drawn to the top A of the mountain.  Let x ft be the length of the cable required from A to D.

 

Consider the Rt triangle ABC in which BC= 3400 Cot74.  Hence BD = 930+3400 Cot74

 

Now consider the  Rt triangle ABD in which,

 

DA2 = (3400)2 + (930 +3400Cot74)2

 

        = (3400)2 + (930+974.938)2

 

            = (3400)2 + (1904.938)2

 

        = 11560000+ 3628788.7838

 

        =15188788.7838

 

Hence DA= 3897.2796 ft

 

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