To find the total distance Nancy has walked around the circular track, let’s follow these steps:
1. Understand the Problem:
- The radius of the circular track is 45 feet.
- Nancy walks 210 degrees around the track.
2. Convert Degrees to Radians:
- Since the arc length formula requires the angle in radians, we convert 210 degrees to radians.
- The conversion formula is: [tex]\( \text{radians} = \text{degrees} \times \left( \frac{\pi}{180} \right) \)[/tex].
3. Calculate Radians Walked:
- For 210 degrees, the calculation is:
[tex]\[
\text{radians} = 210 \times \left( \frac{\pi}{180} \right) = \frac{210\pi}{180} = \frac{21\pi}{18} = \frac{7\pi}{6}
\][/tex]
- Therefore, [tex]\( \frac{7\pi}{6} \approx 3.6652 \)[/tex] radians (rounded to four decimal places).
4. Calculate the Arc Length:
- The arc length [tex]\( L \)[/tex] of a circle is given by the formula: [tex]\( L = r \theta \)[/tex], where [tex]\( r \)[/tex] is the radius and [tex]\( \theta \)[/tex] is the angle in radians.
- Substituting the values, we get:
[tex]\[
L = 45 \times 3.6652 \approx 164.9336 \text{ feet}
\][/tex]
5. Round to the Nearest Foot:
- To the nearest foot, the distance walked is approximately:
[tex]\[
165 \text{ feet}
\][/tex]
Therefore, Nancy has walked 165 feet around the track. You should enter the number "165".
