To convert an angle in degrees to length in feet:
\[ L = \left(\frac{a}{360}\right) \times 2 \pi r \]
Where:
Converting degrees to feet is typically talked about when looking at a circle and converting an angle to the corresponding length of the arc of that angle. Often times that circle is the earth when talking about latitude and longitude.
Let's assume the following values:
Step 1: Divide the angle by 360:
\[ \frac{a}{360} = \frac{45}{360} = 0.125 \]
Step 2: Multiply by 2π:
\[ 0.125 \times 2 \pi \approx 0.125 \times 6.2832 = 0.7854 \]
Step 3: Multiply by the radius:
\[ L = 0.7854 \times 10 = 7.85 \text{ feet} \]
