Answer:
 3902.2 ft
Step-by-step explanation:
You want the length of cable required to span the distance from the top of a mountain 3400 ft above the plain from a location 940 ft from the base of the mountain, which rises at an angle of 74°.
Horizontal distance
The edge of the base of the mountain will be at a horizontal distance from the point below the peak given by ...
 Tan = Opposite/Adjacent
 Adjacent = Opposite/Tan
 width to center = (3400 ft)/tan(74°) ≈ 974.93 . . . . feet
Cable length
The cable is the hypotenuse of a right triangle with one leg 3400 ft and the other (974.93 +940) = 1941.93 ft. The length of that is ...
 c = √(3400² +1914.93²) ≈ 3902.2 . . . . feet
The shortest length of cable needed is about 3902.2 feet.
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