The circular arc of a railroad curve has a chord of length 2

The circular arc of a railroad curve has a chord of length 2500 feet corresponding to central angle of 35 degrees. Find the length of the circular arc.

Solution

chord length = 2500 feet

central angle = 35 degrees

finding radius

2500^2 = r^2 + r^2 - 2r^2 cos 35

2500^2 = 2r^2 - 1.6383r^2

2500^2 = 0.3617r^2

2500 = 0.6014 r

r = 4156.967

circular arc = r* theta

= 4156.967 * 35 * pi/180

= 2538.06

length of circular arc = 2538.06