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Charlie stands at point [tex]\( A \)[/tex] while holding the control line attached to a model airplane. The plane travels 120 feet counterclockwise from point [tex]\( B \)[/tex] to point [tex]\( C \)[/tex]. About how long is the control line?

The control line is about _______.



Answer :

GinnyAnswer
To solve the given problem, we need to determine the length of the control line, which is the radius of the circular path that the model airplane follows.

1. Distance Traveled: The airplane travels 120 feet along a circular path.

2. Circumference of the Circle: The distance of 120 feet is a part of the circumference of the circle. To find the full circumference (C) of the entire path, we double the distance traveled (since a circular path has symmetric properties). Thus, the full circumference is:

[tex]\[ C = 2 \times 120 \text{ feet} = 240 \text{ feet} \][/tex]

3. Formula for Circumference: The circumference [tex]\(C\)[/tex] of a circle is given by the formula:

[tex]\[ C = 2 \pi r \][/tex]

where [tex]\(r\)[/tex] is the radius (the length of the control line).

4. Solving for the Radius: Rearrange the formula to solve for the radius [tex]\(r\)[/tex]:

[tex]\[ r = \frac{C}{2 \pi} \][/tex]

6. Substitute the Known Circumference: Substitute [tex]\(C = 240\)[/tex] feet into the formula:

[tex]\[ r = \frac{240 \text{ feet}}{2 \pi} \][/tex]

7. Calculate the Radius: Perform the division:

[tex]\[ r \approx 38.197186342054884 \text{ feet} \][/tex]

Therefore, the length of the control line is approximately 38.2 feet.

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