A steep mountain is inclined 74 degree to the horizontal and rises to a height of 3400 ft above the surrounding plain. A cable car is to be installed running

Cable length (single strand)  3897.27     ft      (double this (plus a little more for the turn-around) if a loop is going to be installed)

I'm assuming that the cable is not doubled.....

We need to find the length of the base of the mountain =

3400/tan(74)  = about 975 ft

So....the length of the cable  =

sqrt [ 3400^2 + (975 + 930)^2]  = about 3897.3 ft