By arc definition, the radius of a 1° curve is _____ ft.

By arc definition, the radius of a 1° curve is _____ ft.

• A. 1800.50
• B. 5000.00
• C. 5729.58
• D. 6000.00

Answer: (C)

To determine the radius of a 1° curve using the arc definition, we can use the formula which relates the radius to the curve's angle in degrees. The radius \( R \) in feet can be approximated using the formula: \[ R = \frac{5729.58}{\text{Degrees}} \] For a 1° curve, substituting the degree value into this formula gives: \[ R = \frac{5729.58}{1} = 5729.58 \text{ feet} \] This formula stems from the relationship between the length of the arc, the radius, and the angle in a circle, where the constant 5729.58 feet is derived from the conversion factors associated with degrees of arc in relation to the radius of a circle. The correct answer reflects this calculation accurately, reaffirming that for a 1° curve, the radius is conventionally understood to be 5729.58 feet.

To determine the radius of a 1° curve using the arc definition, we can use the formula which relates the radius to the curve's angle in degrees. The radius ( R ) in feet can be approximated using the formula:

[ R = \frac{5729.58}{\text{Degrees}} ]

For a 1° curve, substituting the degree value into this formula gives:

[ R = \frac{5729.58}{1} = 5729.58 \text{ feet} ]

This formula stems from the relationship between the length of the arc, the radius, and the angle in a circle, where the constant 5729.58 feet is derived from the conversion factors associated with degrees of arc in relation to the radius of a circle.

The correct answer reflects this calculation accurately, reaffirming that for a 1° curve, the radius is conventionally understood to be 5729.58 feet.