Explanation:
Relation between length of a curve and angle is as follows.
l = [tex]R \times \Theta[/tex]
where, R = radius of curve
[tex]\Theta[/tex] = angle in radians
Also, l = [tex]R \times \Theta \times \frac{\pi}{180}[/tex] .......... (1)
If curve has a degree of curvature [tex]D_{a}[/tex] for standard length s, then
R = [tex]\frac{s}{D_{a}} \times \frac{180}{\pi}[/tex] ........... (2)
Now, substitute the value of R from equation (2) into equation (1) as follows.
l = [tex]\frac{s \times \Theta}{D_{a}}[/tex]
If s = 30 m, then calculate the value of l as follows.
l = [tex]\frac{s \times \Theta}{D_{a}}[/tex]
= [tex]30 \times \frac{45.2}{3}[/tex]
= 452 m
thus, we can conclude that the length of the curve is 452 m.
