Between Massena and Anaheim there are two railroad tracks. One of them is straight and is 4 miles long. The other one is the arc of a circle and is 5 miles long.

What is the radius of curvature of the curved track?

What you have are the lengths of a chord and the subtended arc of a circle and you need to find the radius.

1)Define a few variables:
R = the unknown radius
θ = the subtended angle (in radians)
A = the arclength of the subtended arc = 5
C = the length of the chord = 4

2) Set up the equations:
A = Rθ =5
sin(θ/2) = (C/2)/R = 2/R

3) Solve for θ:
θ = 5/R = 2(arcsin[2/R])

4) Solve for R

Posted by TomM on 2004-01-07 10:56:16