Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To find the length of the control line Charlie is holding, we need to understand some key pieces of information from the problem:
1. Charlie stands at point A, and the airplane travels 120 feet from point B to point C along an arc that is part of a full circle.
2. This arc length (120 feet) represents a fraction of the entire circle's circumference.
Given that the 120 feet represents a certain fraction of the circle's total circumference, let's assume it's one-fourth (1/4) of the circle since it travels counterclockwise in this way. This means that the full circumference of the circle is:
[tex]\[ \text{Circumference} = 120 \, \text{feet} \times 4 \][/tex]
So the total circumference of the circle is 480 feet.
The formula for the circumference of a circle is:
[tex]\[ \text{Circumference} = 2 \pi \times \text{radius} \][/tex]
We know the circumference is 480 feet. By solving for the radius (which represents the length of the control line), we have:
[tex]\[ \text{radius} = \frac{\text{Circumference}}{2 \pi} \][/tex]
By substituting the circumference value:
[tex]\[ \text{radius} = \frac{480}{2 \pi} \][/tex]
We can now find the radius value:
[tex]\[ \text{radius} \approx \frac{480}{6.2832} \approx 76.39 \, \text{feet} \][/tex]
Therefore, the length of the control line Charlie is holding is about 76.39 feet.
From the given options in the drop-down menu:
The control line is about \( \boxed{76.39437268410977} \) feet long.
Since we need a close answer, and the provided one is not exactly present in the options, we can approximate it to the closest option:
The control line is about [tex]\( 86 \)[/tex] feet long.
1. Charlie stands at point A, and the airplane travels 120 feet from point B to point C along an arc that is part of a full circle.
2. This arc length (120 feet) represents a fraction of the entire circle's circumference.
Given that the 120 feet represents a certain fraction of the circle's total circumference, let's assume it's one-fourth (1/4) of the circle since it travels counterclockwise in this way. This means that the full circumference of the circle is:
[tex]\[ \text{Circumference} = 120 \, \text{feet} \times 4 \][/tex]
So the total circumference of the circle is 480 feet.
The formula for the circumference of a circle is:
[tex]\[ \text{Circumference} = 2 \pi \times \text{radius} \][/tex]
We know the circumference is 480 feet. By solving for the radius (which represents the length of the control line), we have:
[tex]\[ \text{radius} = \frac{\text{Circumference}}{2 \pi} \][/tex]
By substituting the circumference value:
[tex]\[ \text{radius} = \frac{480}{2 \pi} \][/tex]
We can now find the radius value:
[tex]\[ \text{radius} \approx \frac{480}{6.2832} \approx 76.39 \, \text{feet} \][/tex]
Therefore, the length of the control line Charlie is holding is about 76.39 feet.
From the given options in the drop-down menu:
The control line is about \( \boxed{76.39437268410977} \) feet long.
Since we need a close answer, and the provided one is not exactly present in the options, we can approximate it to the closest option:
The control line is about [tex]\( 86 \)[/tex] feet long.
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.