Sam wants to install a zip line across a ravine. one side is of the ravine is 85 feet tall while the other side is 197 feet. if the ravine is 15 feet wide how long must the zip line be?

Refer to the diagram shown below.

Let x =  the length of the zip line.

One side of the ravine is 85 feet tall and the other side is 197 feet tall.
The difference in height is
197 - 85 = 112 feet, as shown in the figure.

Apply the Pythagorean theorem to the right triangular portion of the figure.
x² = 15² + 112²
    = 12769
x = √(12769)
   = 113 ft

The length of the zip line is 113 feet.