Question

How long is the control line? I couldn’t figure this out

Answer 1

Given the circle with center A as shown below:

The plane travels 120 feet counterclockwise from B to C, thus forming an arc AC.

The length of the arc AC is expressed as

`\begin{gathered} L=(\theta)/(360)*2\pi r \\ \text{where} \\ \theta\Rightarrow angle\text{ (in degre}e)\text{subtended at the center of the circle} \\ r\Rightarrow radius\text{ of the circle, which is the }length\text{ of the control line} \\ L\Rightarrow length\text{ of the arc AC} \end{gathered}`

Given that

`\begin{gathered} L=120\text{ f}eet \\ \theta=80\degree \\ \end{gathered}`

we have

`\begin{gathered} L=(\theta)/(360)*2\pi r \\ 120=(80)/(360)*2*\pi* r \\ cross\text{ multiply} \\ 120*360=80*2*\pi* r \\ \text{make r the subject of the equation} \\ \Rightarrow r=(120*360)/(2*\pi*80) \\ r=85.94366927\text{ fe}et \end{gathered}`

Hence, the length of the control line is 85.94366927 feet.