Question

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 to the top of the mountain from a point 940 ft out in the plain from the base of the mountain. Find the shortest length of cable needed.

Answer 1

3902.2 ft

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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