Question

The figure below shows the ideal pattern of movement of a herd of cattle, with the arrows showing the movement of the handler as he moves the herd. The arc the handler makes from the starting point to the return point should be a quarter of a circle.. . . . Based on this theory, what distance will the handler move from the starting point to the return point if he creates an arc of a circle of radius 85 feet?. Answer. 21.25. 66.73 feet. 88.97 feet. 133.45 feet.

Answer 1

The arc length in degrees (same as central angle that cuts it off) is to 360 (degrees in a circle) AS the arc length in linear measure is to the circumference of the circle (2 pi r).
90/360 = AL/[2 pi (85)] where AL is the arc length in linear measure.
 1/4 = AL/[170 pi]
4 AL = 170 pi
 AL = 42.5 pi
 AL = 133.45 feet (approx)

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