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:

A sector showing a quarter of a circle is drawn. The radius is marked as 75 feet. The endpoints of the arc of the sector are marked as Starting Point and Return Point. The sector is filled with cattle.

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 with radius 75 feet?
1884 feet
4415.63 feet
58.88 feet
117.75 feet

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akposevictor akposevictor · Answer 1 · 2022-04-21T12:18:08+02:00

Based on the theory, the distance from the starting point to the return point = Arc length = 117.75 feet.

Arc length = ∅/360 × 2πr

Since the sector formed is a quarter circle, then ∅ = 90°.

Raidus (r) = 75 ft

Distance from the starting point to the return point = arc length.

Arc length = ∅/360 × 2πr = 90/360 × 2π(75)

Arc length = 117.75 feet

Therefore, based on the theory, the distance from the starting point to the return point = Arc length = 117.75 feet.

Learn more about the arc length on:

https://brainly.com/question/2005046

AFOKE88 AFOKE88 · Answer 2 · 2022-04-27T14:47:38+02:00

Based on the theory, the distance from the starting point to the return point if he creates an arc with a radius of 75 ft is; D: 117.75 feet.

From the given attached image, we can see that the pattern of movement of a herd of cattle forms a sector. Formula for arc length of a sector is;

Arc length = (θ/360) × 2πr

We are told that The arc the handler makes from the starting point to the return point should be a quarter of a circle. Thus;

θ = 90°.

Radius is given as; r = 75 ft

Arc length = (90/360) × 2π(75)

Arc length = 117.75 feet

Now, the distance from the starting point to the return point is same as the Arc length. Thus;

The Distance from the starting point to the return point = 117.75 feet.

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