Avertical pole 27 feet tall stands on a hillside that makes an angle of 19o with the horizontal. determine the approximate length of cable that would be needed to reach from the top of the pole to a point 80 feet downhill from the base of the pole. round answer to two decimal places.

The hill describes a right triangle with the position of the cable (the base) = 80ft and makes an angle of 19° with the horizontal.
Let the height of the hill be x.
tan 19° = x/80
x = 80 tan 19° = 27.5462
The height of the hill and the pole = 27 + 27.5462 = 54.5462
The required length of the cable is given by sqrt(80^2 + 54.5462^2) = sqrt(6400 + 2975.2889) = sqrt(9375.2889) = 96.83 feet.

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