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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? (6 points)


21.25

133.45 feet

66.73 feet

88.97 feet

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 Ha class=

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Answer:

B)  133.45 ft

Step-by-step explanation:

The arc the handler makes from the starting point to the return point is a quarter of a circle.

The length of the arc of a quarter circle is equivalent to one quarter of the circle's circumference.

The formula for the circumference of a circle with radius r is C = 2πr. Therefore, the formula for the arc of a quarter circle (s) is:

[tex]s=\dfrac{2\pi r}{4}=\dfrac{\pi r}{2}[/tex]

To find the length of the arc, substitute the radius r = 85 ft  into the formula and use π = 3.14:

[tex]s=\dfrac{3.14 \cdot 85}{2} \\\\\\ s=\dfrac{266.9}{2} \\\\\\ s=133.45\; \sf ft[/tex]

Therefore, the distance the handler will move is:

[tex]\LARGE\boxed{\sf 133.45 \; ft}[/tex]

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