Question

Help!!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
https://vvsd6966-vvagpeap-ccl.gradpoint.com/Resource/6114359,67D,0,0,0,0,0/Assets/74874_53c6cf97/image0024e68d49d.jpg
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 75 feet?
1884 feet
4415.63 feet
58.88 feet
117.75 feet
1884?

Answer 1

@inkyvoyd @Directrix @dan815

Answer 2

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 (75)] where AL is the arc length in linear measure.

1/4 = AL/[150 pi]
4 AL = 150 pi
AL = 37.5 pi
AL = 117.81 feet (approx)

@Tatsurion Check my work

Answer 3

Omg openstudy is lagging......

Answer 4

Seems about right.