How do you find the r and s of a circular arc that has 3000 feet of chord length and a central angle of 40de?

Question

The circular arc of a railroad that has a chord of length 3000 feet and a central angle of 40 degrees. The (r) and (s) are the radius and the length of the arc respectively.

Answer 1

The radius is = 1500 /sin 20 degrees= 4385.7066 feet
s = r*theta where theta = 40 degrees = 40pi/180 radians
s= 4385.7066*2pi/9 = 3,060.25 feet.

Note that the perpendicular bisector of the chord passes through the center of the circle so a right triangle is formed with hypotenuse = r, short leg = 3000/2 =1500 and an angle opposite the short = 40/2 = 20 degrees.