First we can find the circumference of the whole circle with a radius of 5 feet.
circumference = 2 pi radius
circumference = (2 pi) (5 feet)
circumference = (10 pi) feet
From one high point to the other high point, the string moves through an angle of 10 degrees. Since a full circle is 360 degrees, this angle is 1/36 of a full circle.
Therefore, the arc length is 1/36 of the whole circumference.
arc length = (1/36) (circumference)
arc length = (1/36) (10 pi) feet
arc length = 0.873 feet
